Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning 2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
On 30/06/2024 8:44 am, Cursitor Doom wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
Watch this (your question is addressed at 2:07)
<https://youtu.be/Vv2W5vJFqFo?si=eX3ZONUzzpNNxGtg>
piglet
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning >2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom <cd@notformail.com>
wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning >>2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
2 * pi.
If a thing 1 unit in radius rotates one time per second, its
circumference is 2pi so its rim velocity is 2pi/second.
A capacitor current depends on the rate of change of the voltage.
I = CV/T
A 1 volt peak 1 Hz sine wave has its max rate of change at the zero >crossing, and that rate is 2pi volts/second. So 1 farad driven with a
1 Hz 1 volt peak sine wave has a peak current of 2pi amps.
You can Spice all that to get a feel for things.
On Sun, 30 Jun 2024 11:57:21 +0100, piglet <erichpwagner@hotmail.com>
wrote:
On 30/06/2024 8:44 am, Cursitor Doom wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
Watch this (your question is addressed at 2:07)
<https://youtu.be/Vv2W5vJFqFo?si=eX3ZONUzzpNNxGtg>
Thanks, Erich. I did wonder if radians had something to do with it.
However, knowing that 2 pi radians = 360 degrees or a full wavelength
doesn't help me understand why this figure multiplied by the frequency multiplied by the inductance gives us the reactance of a coil. Small
omega therefore equals one second's worth of signal and I don't get
how multipying that by the inductance amounts to the reactance!
On 2024-06-30 03:44, Cursitor Doom wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
As an old colleague of mine from grad school would say, "It just comes
out in the math." ;)
The 2*pi factor comes from the time domain / frequency domain
conversion, and the basic behavior of linear differential equations with constant coefficients. (That's magic.(*)) For now we'll just talk about
LR circuits and pulses.
A 1-second pulse (time domain) has an equivalent width of 1 Hz
(frequency domain, including negative frequencies). That's pretty
intuitive, and shows that seconds and cycles per second are in some
sense the same 'size'. The two scale inversely, e.g. a 1-ms pulse has
an equivalent width of 1 kHz, also pretty intuitive. (Equivalent width
is the mathematical quantity for which this 1-Hz/1-s inverse relation
holds exactly, independent of the shape of the waveform.)
Moving gently towards the frequency domain, we have the ideas of
resistance and reactance. Resistance is defined by
V = IR, (1)
independent of both time and frequency. Actual resistors generally
behave very much that way, over some reasonable range of frequencies and power levels. Either V or I can be taken as the independent variable,
i.e. the one corresponding to the dial setting on the power supply, and
the equation gives you the other (dependent) variable.
A 1-Hz sine wave of unit amplitude at frequency f is given by
I = sin(2 pi f t), (2)
and the reactance of an inductance L is
X = 2 pi f L. (3)
The reactance is analogous to resistance, except that since inductance couples to dI/dt rather than I. From the definition of inductance,
V = L dI/dt. (4)
Plugging (2) into (4), you get
V = L dI/dt = L * (2 pi f) cos(2 pi f t) = X_L cos(2 pi f t), (5)
where X_L is the inductive reactance.
We see that the voltage dropped by the inductance is phase shifted by
1/4 cycle. Since the cosine reaches its peak at 0, where the current
(the independent variable) is just going positive, we can say that the voltage waveform is _advanced_ by a quarter cycle, i.e. that the voltage
is doing what the imposed current was doing a quarter cycle previously.
(This seems like a fine point, but it's crucial to keeping the sign of
the phase shift right, especially when you're a physics/engineering
amphibian like me--the two disciplines use opposite sign conventions.)
Besides the phase shift, the voltage across the inductance has an extra factor of 2 pi f. This is often written as a Greek lowercase omega,
which for all you slipshod HTML-mode types is ω = 2πf.
Writing the sine wave as
I = sin(ωt) (6)
is faster, but the factor of 2 pi in amplitude keeps coming up, which it inescapably must, and it doesn't even really simplify the math much.
For instance, if we apply a 1-V step function across a series RL with a
time constant
tau = L/R = 1 second, (7)
the voltage on the resistor is
V = 1-exp(-t). (8)
In the frequency domain, the phase shift makes things a bit more
complicated. If we use our nice real-valued sinusoidal current waveform
(6) that we can see on a scope, then (after a small flurry of math), the voltage on the resistor comes out as
V = sin(t - arctan(omega L/R)) / sqrt(1 + (omega L / R)**2). (9)
This is because sines and cosines actually are sums of components of
both positive and negative frequency, and which don't behave the same
way when you differentiate them:
sin(omega t) = 1/2 * (exp(j omega t) - exp(-j omega t)) (10)
and
cos(omega t) = 1/2 * (exp(j omega t) + exp(-j omega t)). (11)
By switching to complex notation, and making a gentlemen's agreement to
take the real part of everything before we start predicting actual
measurable quantities, the math gets much simpler. Our sinusoidal input voltage becomes
Vin = exp(j omega t) (12)
and the voltage across the resistor is just the voltage divider thing:
V/Vin = R / (R + j omega L). (13)
At low frequencies, the resistance dominates and the inductance doesn't
do anything much, just a small phase shift
theta ~= - j omega L/R.
At high frequencies, the inductance dominates. In the middle, the two effects become comparable at a frequency
omega0 = R/L.
At that frequency, the phase shift is -45 degrees and the amplitude is
down by 1/sqrt(2) (-3 dB) and the power dissipated in the resistor falls
to half of its DC value.
If we're using the series LR as a lowpass filter, that's the frequency
that divides the passband, where the signal mostly gets through, from
the stopband, where it mostly doesn't.
So when we think in the time domain, a 1-ohm/1-henry LR circuit responds
in about a second, whereas in the frequency domain, its bandwidth rolls
off at omega = 1, i.e. at 1/(2 pi) Hz.
With sinusoidal waveforms, we can think of 1 second corresponding to 1
radian per second, whereas with pulses, a 1 second pulse has a 1-Hz-wide spectrum (counting negative frequencies).
Thing is, a sine wave varies smoothly and goes through a much more complicated evolution (positive to negative and back) within a cycle, so
it just takes longer, by a factor that turns out to be 2*pi.
Cheers
Phil Hobbs
(*) Kipling, "How the Rhinoceros got his skin"
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning 2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom <cd@notformail.com> >>wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning >>>2*pi*the-frequency-of-interest rather than the large Omega which is >>>already reserved for Ohms. How does it keep cropping up? What's so >>>special about the constant 6.283 and from what is it derived?
Just curious...
2 * pi.
If a thing 1 unit in radius rotates one time per second, its
circumference is 2pi so its rim velocity is 2pi/second.
A capacitor current depends on the rate of change of the voltage.
I = CV/T
A 1 volt peak 1 Hz sine wave has its max rate of change at the zero >>crossing, and that rate is 2pi volts/second. So 1 farad driven with a
1 Hz 1 volt peak sine wave has a peak current of 2pi amps.
You can Spice all that to get a feel for things.
Thanks, John. This is the fundamental stuff I just overlook since the
need for it so rarely crops up. It's easier to take an abstraction
level higher and lose all the vital detail in the process.
You're up early today. Off to church are we?
Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> wrote:
On 2024-06-30 03:44, Cursitor Doom wrote:Belay that last bit—it’s exactly backwards. I’ll fix it when I get back from church.
Gentlemen,As an old colleague of mine from grad school would say, "It just comes
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
out in the math." ;)
The 2*pi factor comes from the time domain / frequency domain
conversion, and the basic behavior of linear differential equations
with constant coefficients. (That's magic.(*)) For now we'll just talk
about LR circuits and pulses.
A 1-second pulse (time domain) has an equivalent width of 1 Hz
(frequency domain, including negative frequencies). That's pretty
intuitive, and shows that seconds and cycles per second are in some
sense the same 'size'. The two scale inversely, e.g. a 1-ms pulse has
an equivalent width of 1 kHz, also pretty intuitive. (Equivalent width
is the mathematical quantity for which this 1-Hz/1-s inverse relation
holds exactly, independent of the shape of the waveform.)
Moving gently towards the frequency domain, we have the ideas of
resistance and reactance. Resistance is defined by
V = IR, (1)
independent of both time and frequency. Actual resistors generally
behave very much that way, over some reasonable range of frequencies
and power levels. Either V or I can be taken as the independent
variable, i.e. the one corresponding to the dial setting on the power
supply, and the equation gives you the other (dependent) variable.
A 1-Hz sine wave of unit amplitude at frequency f is given by
I = sin(2 pi f t), (2)
and the reactance of an inductance L is
X = 2 pi f L. (3)
The reactance is analogous to resistance, except that since inductance
couples to dI/dt rather than I. From the definition of inductance,
V = L dI/dt. (4)
Plugging (2) into (4), you get
V = L dI/dt = L * (2 pi f) cos(2 pi f t) = X_L cos(2 pi f t), (5)
where X_L is the inductive reactance.
We see that the voltage dropped by the inductance is phase shifted by
1/4 cycle. Since the cosine reaches its peak at 0, where the current
(the independent variable) is just going positive, we can say that the
voltage waveform is _advanced_ by a quarter cycle, i.e. that the
voltage is doing what the imposed current was doing a quarter cycle
previously. (This seems like a fine point, but it's crucial to keeping
the sign of the phase shift right, especially when you're a
physics/engineering amphibian like me--the two disciplines use opposite
sign conventions.)
Besides the phase shift, the voltage across the inductance has an extra
factor of 2 pi f. This is often written as a Greek lowercase omega,
which for all you slipshod HTML-mode types is ω = 2πf.
Writing the sine wave as
I = sin(ωt) (6)
is faster, but the factor of 2 pi in amplitude keeps coming up, which
it inescapably must, and it doesn't even really simplify the math much.
For instance, if we apply a 1-V step function across a series RL with a
time constant
tau = L/R = 1 second, (7)
the voltage on the resistor is
V = 1-exp(-t). (8)
In the frequency domain, the phase shift makes things a bit more
complicated. If we use our nice real-valued sinusoidal current
waveform (6) that we can see on a scope, then (after a small flurry of
math), the voltage on the resistor comes out as
V = sin(t - arctan(omega L/R)) / sqrt(1 + (omega L / R)**2). (9)
This is because sines and cosines actually are sums of components of
both positive and negative frequency, and which don't behave the same
way when you differentiate them:
sin(omega t) = 1/2 * (exp(j omega t) - exp(-j omega t)) (10)
and
cos(omega t) = 1/2 * (exp(j omega t) + exp(-j omega t)). (11)
By switching to complex notation, and making a gentlemen's agreement to
take the real part of everything before we start predicting actual
measurable quantities, the math gets much simpler. Our sinusoidal
input voltage becomes
Vin = exp(j omega t) (12)
and the voltage across the resistor is just the voltage divider thing:
V/Vin = R / (R + j omega L). (13)
At low frequencies, the resistance dominates and the inductance doesn't
do anything much, just a small phase shift
theta ~= - j omega L/R.
At high frequencies, the inductance dominates. In the middle, the two
effects become comparable at a frequency
omega0 = R/L.
At that frequency, the phase shift is -45 degrees and the amplitude is
down by 1/sqrt(2) (-3 dB) and the power dissipated in the resistor
falls to half of its DC value.
If we're using the series LR as a lowpass filter, that's the frequency
that divides the passband, where the signal mostly gets through, from
the stopband, where it mostly doesn't.
So when we think in the time domain, a 1-ohm/1-henry LR circuit
responds in about a second, whereas in the frequency domain, its
bandwidth rolls off at omega = 1, i.e. at 1/(2 pi) Hz.
With sinusoidal waveforms, we can think of 1 second corresponding to 1
radian per second, whereas with pulses, a 1 second pulse has a
1-Hz-wide spectrum (counting negative frequencies).
Thing is, a sine wave varies smoothly and goes through a much more
complicated evolution (positive to negative and back) within a cycle,
so it just takes longer, by a factor that turns out to be 2*pi.
Cheers
Phil Hobbs
(*) Kipling, "How the Rhinoceros got his skin"
Cheers
Phil Hobbs
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom <cd@notformail.com>rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin <jlarkin_highland_tech> >>wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom <cd@notformail.com> >>>wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without >>>>even giving a thought as to how omega gets involved in so many aspects >>>>of RF. BTW, that's a lower-case, small omega meaning >>>>2*pi*the-frequency-of-interest rather than the large Omega which is >>>>already reserved for Ohms. How does it keep cropping up? What's so >>>>special about the constant 6.283 and from what is it derived?
Just curious...
2 * pi.
If a thing 1 unit in radius rotates one time per second, its >>>circumference is 2pi so its rim velocity is 2pi/second.
A capacitor current depends on the rate of change of the voltage.
I = CV/T
A 1 volt peak 1 Hz sine wave has its max rate of change at the zero >>>crossing, and that rate is 2pi volts/second. So 1 farad driven with a 1 >>>Hz 1 volt peak sine wave has a peak current of 2pi amps.
You can Spice all that to get a feel for things.
Thanks, John. This is the fundamental stuff I just overlook since the
need for it so rarely crops up. It's easier to take an abstraction level >>higher and lose all the vital detail in the process.
It's good to understand the basics, but I mostly use Spice these days,
even for simple things like voltage dividers.
You're up early today. Off to church are we?
No, I just woke up early with a zillion ideas. That happens some times.
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's a
good day to stay close to home. Traffic and parking and everything will
be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/Pink_Triangle.jpg?
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning 2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
On 6/30/2024 3:44 AM, Cursitor Doom wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae such
as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without even
giving a thought as to how omega gets involved in so many aspects of
RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
You've had a number of answers - but not really answering at the "gut"
level. Why is 2 pi so important - how does omega get involved in so
many aspects of RF?
Every one of the formulas you mentioned has to do with frequency.
The unit of measurement for that is Hertz which is CYCLE(s) per second.
A cycle's length is 360 degrees regardless of frequency.
A CIRCLE's length is 360 degrees regardless of frequency.
A circle's length is also 2*pi*r regardless of frequency. Therefore a
CYCLE's length (a.k.a wavelength a.k.a. omega)
is also 2*pi*r long.
So 2*pi is used in the conversion between the number of degrees (time)
and distance (length displacement) or "How much happened ?" (length displacement)
"and how long did it take?" time (frequency).
That's what some call the "gut level" understanding aas to why 2*pi
appears so often. If you use the math a lot over time it becomes less mysterious - if that's the right term. I guess you develop an intuitive understanding or something like that.
Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> wrote:
On 2024-06-30 03:44, Cursitor Doom wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom <cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin <jlarkin_highland_tech>
wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom <cd@notformail.com>
wrote:
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's arlkey=n4xinzzm39bms9w04syb7egkx&raw=1
good day to stay close to home. Traffic and parking and everything will
be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God almighty!
I've never seen such a complete and utter freak show in my entire life. I just stood there gaping open-mouthed at the procession. It must have been pretty obvious to any of those weirdos on the floats that I wasn't there
to celebrate them! I just find it bizarre that parents actually take their kids to see this sort of thing and they're all waving their rainbow flags
and whatnot. No kids of mine would be allowed within a million miles of an event like that. No wonder the God-fearing folks reckon the world's going
to hell in a handbasket. :(
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom <cd@notformail.com>rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin <jlarkin_highland_tech>
wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom <cd@notformail.com>
wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects >>>>> of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
2 * pi.
If a thing 1 unit in radius rotates one time per second, its
circumference is 2pi so its rim velocity is 2pi/second.
A capacitor current depends on the rate of change of the voltage.
I = CV/T
A 1 volt peak 1 Hz sine wave has its max rate of change at the zero
crossing, and that rate is 2pi volts/second. So 1 farad driven with a 1 >>>> Hz 1 volt peak sine wave has a peak current of 2pi amps.
You can Spice all that to get a feel for things.
Thanks, John. This is the fundamental stuff I just overlook since the
need for it so rarely crops up. It's easier to take an abstraction level >>> higher and lose all the vital detail in the process.
It's good to understand the basics, but I mostly use Spice these days,
even for simple things like voltage dividers.
You're up early today. Off to church are we?
No, I just woke up early with a zillion ideas. That happens some times.
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's a
good day to stay close to home. Traffic and parking and everything will
be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God almighty!
I've never seen such a complete and utter freak show in my entire life. I just stood there gaping open-mouthed at the procession. It must have been pretty obvious to any of those weirdos on the floats that I wasn't there
to celebrate them! I just find it bizarre that parents actually take their kids to see this sort of thing and they're all waving their rainbow flags
and whatnot. No kids of mine would be allowed within a million miles of an event like that. No wonder the God-fearing folks reckon the world's going
to hell in a handbasket. :(
On 6/30/2024 12:45 PM, Cursitor Doom wrote:Pink_Triangle.jpg?
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom <cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae >>>>>> such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without >>>>>> even giving a thought as to how omega gets involved in so many
aspects of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is >>>>>> already reserved for Ohms. How does it keep cropping up? What's so >>>>>> special about the constant 6.283 and from what is it derived?
Just curious...
2 * pi.
If a thing 1 unit in radius rotates one time per second, its
circumference is 2pi so its rim velocity is 2pi/second.
A capacitor current depends on the rate of change of the voltage.
I = CV/T
A 1 volt peak 1 Hz sine wave has its max rate of change at the zero >>>>> crossing, and that rate is 2pi volts/second. So 1 farad driven with
a 1 Hz 1 volt peak sine wave has a peak current of 2pi amps.
You can Spice all that to get a feel for things.
Thanks, John. This is the fundamental stuff I just overlook since the
need for it so rarely crops up. It's easier to take an abstraction
level higher and lose all the vital detail in the process.
It's good to understand the basics, but I mostly use Spice these days,
even for simple things like voltage dividers.
You're up early today. Off to church are we?
No, I just woke up early with a zillion ideas. That happens some
times.
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's a
good day to stay close to home. Traffic and parking and everything
will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
I went to one of those once in Berlin when I lived there. God almighty!
I've never seen such a complete and utter freak show in my entire life.
I just stood there gaping open-mouthed at the procession. It must have
been pretty obvious to any of those weirdos on the floats that I wasn't
there to celebrate them! I just find it bizarre that parents actually
take their kids to see this sort of thing and they're all waving their
rainbow flags and whatnot. No kids of mine would be allowed within a
million miles of an event like that. No wonder the God-fearing folks
reckon the world's going to hell in a handbasket. :(
Could always move to places that tolerate that sort of stuff. Saudi
Arabia. Moscow. Abilene, Texas. Lots of options.
But Mr. Larkin seems to prefer it in San Fran and you seem to prefer
flitting about western Europe, interesting.
On 2024-06-30 09:51, Phil Hobbs wrote:
Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> wrote:Okay, once more with feelin'. Hopefully this is a bit more coherent throughout.
On 2024-06-30 03:44, Cursitor Doom wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many
aspects of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
As an old colleague of mine from grad school would say, "It just comes
out in the math." ;)
The 2*pi factor comes from the time domain / frequency domain
conversion, and the basic behavior of linear differential equations with constant coefficients. (That's magic.(*)) Pardon my waving my arms a bit--that way we can avoid DEs and Fourier integrals. Here goes.
A 1-second pulse (time domain) has an equivalent width of 1 Hz
(frequency domain, including negative frequencies). That's pretty
intuitive, and shows that seconds and cycles per second are in some
sense the same 'size'. The two scale inversely, e.g. a 1-ms pulse has
an equivalent width of 1 kHz, also pretty intuitive.
Moving gently towards the frequency domain, we have the ideas of
resistance and reactance. Resistance is defined by
V = IR, (1)
independent of both time and frequency. Actual resistors generally
behave very much that way, over some reasonable range of frequencies and power levels. Either V or I can be taken as the independent variable,
i.e. the one corresponding to the dial setting on the power supply, and
the equation gives you the other (dependent) variable.
A 1-Hz sine wave of unit amplitude at frequency f is given by
I = sin(2 pi f t), (2)
and the reactance of an inductance L is
X = 2 pi f L. (3)
The reactance is analogous to resistance, except that inductance couples
to dI/dt rather than I. This comes right out of the definition of inductance,
V = L dI/dt. (4)
Plugging (2) into (4), you get
V = L dI/dt = L * (2 pi f) cos(2 pi f t). (5)
We see that the voltage dropped by the inductance is phase shifted by
1/4 cycle.
Since the cosine reaches its peak at 0, where the current (the
independent variable) is just going positive, we can say that the
voltage waveform is _advanced_ by a quarter cycle, i.e. that the voltage
is doing what the imposed current was doing a quarter cycle previously.
(**)
Besides the phase shift, the voltage across the inductance has an extra factor of 2 pi f. This is often written as a Greek lowercase omega,
which for all you supercool HTML-mode types is ω = 2πf. The
factor ωL comes in exactly the same way as resistance, except for
the frequency dependence and quarter-cycle phase shift, so it's called _reactance_, as noted above.
Writing the sine wave as
I = sin(ωt) (6)
is faster, but the factor of 2 pi in amplitude keeps coming up, which it inescapably must, and it doesn't even really simplify the math much.
(Once you get to Fourier transforms, keeping the 2*pi explicit saves
many blunders, it turns out.)
For instance, if we apply a 1-V step function across a series RL with a
time constant
tau = L/R = 1 second, (7)
the voltage on the resistor is
V = 1-exp(-t). (8)
This rises from 0 to ~0.63 in 1s, 0.9 in 2.3s, and 0.95 in 3.0s.
In the frequency domain, the phase shift makes things a bit more
complicated. If we use our nice real-valued sinusoidal current waveform
(6) that we can see on a scope, then (after a small flurry of math), the voltage on the resistor comes out as
V = sin(t - arctan(omega L/R)) / sqrt(1 + (omega L / R)**2). (9)
This is because sines and cosines actually are sums of components of
both positive and negative frequency, which don't behave the same way
when you differentiate them:
sin(omega t) = 1/2 * (exp(j omega t) - exp(-j omega t)) (10)
and
cos(omega t) = 1/2 * (exp(j omega t) + exp(-j omega t)). (***) (11)
By switching to complex notation and making a gentlemen's agreement to
take the real part of everything before we start predicting actual
measurable quantities, the math gets much simpler. Our sinusoidal input voltage becomes
Vin = exp(j omega t) (12)
and the voltage across the resistor is just the voltage divider thing:
V/Vin = R / (R + j omega L). (13)
At low frequencies, the resistance dominates and the inductance doesn't
do anything much, just a small linear phase shift with frequency
theta ~= - j omega L/R. (14)
At high frequencies, the inductance dominates. In the middle, the two effects become comparable at a frequency
omega0 = R/L.
At that frequency, the phase shift is -45 degrees and the amplitude is
down by 1/sqrt(2) (-3 dB) and the power dissipated in the resistance
falls to half of its DC value.
If we're using the series LR as a lowpass filter, omega_0 is the
frequency that divides the passband, where the signal mostly gets
through, from the stopband, where it mostly doesn't. It's worth noting
that if you extrapolate the low-frequency straight line (14), it passes through 1 radian at omega_0 as well.
So when we think in the time domain, a 1-ohm/1-henry LR circuit responds
in about a second, whereas in the frequency domain, its bandwidth rolls
off at omega = 1, i.e. at 1/(2 pi) Hz.
<Correcting brain fart due to trying to do too many things at once>
Thus with sinusoidal waveforms, we can think of 1 second corresponding
to 1 radian per second, whereas with pulses, a 1 second pulse has a
1-Hz-wide spectrum (counting negative frequencies). Weird, right? What's
up with that?
One way of understanding it is that a square pulse has a lot more high-frequency components than a sine wave. To make our 1-s decaying exponential resemble a 1-s pulse a bit more closely, we need it to start
from 0 and go back to 0. A first try would be making it symmetric.
That costs you in bandwidth, because going up takes as long as going
down, so you have to speed up the time constant.
If we speed it up by a factor of 2, the amplitude reaches 1-exp(-1) ~=
0.63V before starting down again. By the inverse scaling relation, that doubles the bandwidth, getting us to 2 rad/s. To make it a bit more square-looking, we could speed it up some more. Getting up to 90% of
full amplitude takes 2.2 time constants, which notionally takes us to
4.4 rad/s.
Someplace in there we have to start using Fourier integrals, because otherwise we'll start thinking that a perfectly square pulse has
infinite bandwidth, which it doesn't. To avoid that, perhaps you'll
take my word that some more math will show that an actually rectangular
pulse gets you up to 2*pi rad/s, i.e. 1 Hz.
Cheers
Phil Hobbs
(*) Rudyard Kipling, "How the rhinoceros got his skin", in *Just So
Stories*, Macmillan, 1902.
(**) This seems like a fine point, but it's crucial to keeping the sign
of the phase shift right, especially when you're a physics/engineering amphibian like me--in physics an advance is a negative phase shift,
whereas in EE it's positive, owing to different sign conventions.
(***) Here I've adopted the EE sign convention, and so am using 'j' for
the corresponding square root of -1. I use 'i' in physics and math discussions, and that helps keeps everything straight.
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning 2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:Pink_Triangle.jpg?
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom <cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
For more decades than I care to remember, I've been using formulae >>>>>>> such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without >>>>>>> even giving a thought as to how omega gets involved in so many
aspects of RF. BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is >>>>>>> already reserved for Ohms. How does it keep cropping up? What's so >>>>>>> special about the constant 6.283 and from what is it derived?
Just curious...
2 * pi.
If a thing 1 unit in radius rotates one time per second, its
circumference is 2pi so its rim velocity is 2pi/second.
A capacitor current depends on the rate of change of the voltage.
I = CV/T
A 1 volt peak 1 Hz sine wave has its max rate of change at the zero >>>>>> crossing, and that rate is 2pi volts/second. So 1 farad driven with >>>>>> a 1 Hz 1 volt peak sine wave has a peak current of 2pi amps.
You can Spice all that to get a feel for things.
Thanks, John. This is the fundamental stuff I just overlook since the >>>>> need for it so rarely crops up. It's easier to take an abstraction
level higher and lose all the vital detail in the process.
It's good to understand the basics, but I mostly use Spice these days, >>>> even for simple things like voltage dividers.
You're up early today. Off to church are we?
No, I just woke up early with a zillion ideas. That happens some
times.
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's a
good day to stay close to home. Traffic and parking and everything
will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
I went to one of those once in Berlin when I lived there. God almighty!
I've never seen such a complete and utter freak show in my entire life.
I just stood there gaping open-mouthed at the procession. It must have
been pretty obvious to any of those weirdos on the floats that I wasn't
there to celebrate them! I just find it bizarre that parents actually
take their kids to see this sort of thing and they're all waving their
rainbow flags and whatnot. No kids of mine would be allowed within a
million miles of an event like that. No wonder the God-fearing folks
reckon the world's going to hell in a handbasket. :(
Could always move to places that tolerate that sort of stuff. Saudi
Arabia. Moscow. Abilene, Texas. Lots of options.
But Mr. Larkin seems to prefer it in San Fran and you seem to prefer
flitting about western Europe, interesting.
Well, I did warn John about moving to SF many years ago as I could tell
the way it was going, but he went ahead anyway and seems to have an
uncanny ability to only notice the nice side of the place (mainly by not >venturing downtown, it seems).
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom <cd@notformail.com> wrote:the part of the circle circumference between the two lines) divided by the radius. So if a single line rotates one complete revolution it rotates 2.PI radians.
Gentlemen,
For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF. BTW, that's a lower-case, small omega meaning >>2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...
What you are really asking (but may not realise) is why do mathematicians measure an angle in radians. If you draw two straught lines from the origin of a circle to its edge, then the angle (in radians) between the lines is the arc length (length of
One important thing to note is that if an angle x is measured in radians then the limit of sin(x)/x as x goes to 0 is 1. This leads to the derivative (wrt x) of sin(x) being equal to cos(x). *This is not true is x is not specified in radians*. (Italso leads to simple series expansions of the trigonometric fuctions, to eulers formula etc.)
When performing calculus it is thus easiest to do so if angles are measured in radians. For a signal of frequency f it's corresponding phasor representation will rotate by 2.PI.f.t radians in an interval t. This is where the 2.PI comes from in yourcalculations.
For example for your inductor L the voltage across it and the current through it are related by e=L.di/dt. If the current i=I.sin(wt) (w in rad/s) then e=wLI.cos(wt). Thus the impedance e/i is wL cos(wt)/sin(wt) ie. it has a magnitude of wL (or 2.PI.f.L )and a phase angle of PI/2. And so forth.
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom <cd999666@notformail.com> wrote:...
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom <cd@notformail.com> >>>>> wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's a >>>>> good day to stay close to home. Traffic and parking and everything
will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God almighty! >>>> I've never seen such a complete and utter freak show in my entire life. >>>> I just stood there gaping open-mouthed at the procession.
It must have
been pretty obvious to any of those weirdos on the floats that I wasn't >>>> there to celebrate them!
I just find it bizarre that parents actually
take their kids to see this sort of thing and they're all waving their >>>> rainbow flags and whatnot.
No kids of mine would be allowed
within a
million miles of an event like that. No wonder the God-fearing folks
reckon the world's going to hell in a handbasket. :(
Could always move to places that tolerate that sort of stuff. Saudi
Arabia. Moscow. Abilene, Texas. Lots of options.
But Mr. Larkin seems to prefer it in San Fran and you seem to prefer
flitting about western Europe, interesting.
Well, I did warn John about moving to SF many years ago as I could tell
the way it was going, but he went ahead anyway and seems to have an
uncanny ability to only notice the nice side of the place (mainly by not >>venturing downtown, it seems).
You warned me? What's your real name?
When I decided to move to SF, my friends said "But it's full of gay
guys" to which I replied "and lots of smart beautiful women."
Do the math on that.
Right, we avoid the tourist traps and homeless encampments. The hills separate SF into a collection of villages, with even different
weather.
It's a great place to be weird. People get it.
But 2*pi is still 2*pi even here.
"john larkin" <jlarkin_highland_tech> wrote in message news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom <cd@notformail.com> >>>>>> wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's a >>>>>> good day to stay close to home. Traffic and parking and everything >>>>>> will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God almighty! >>>>> I've never seen such a complete and utter freak show in my entire life. >>>>> I just stood there gaping open-mouthed at the procession.
Why were you at the procession? Why did you not stay at home or away from the procession?
Or was it that the procession passed your home?
It must have
been pretty obvious to any of those weirdos on the floats that I wasn't >>>>> there to celebrate them!
Why would that have been obvious to them?
I just find it bizarre that parents actually
take their kids to see this sort of thing and they're all waving their >>>>> rainbow flags and whatnot.
No kids of mine would be allowed
You could find that they remember you for that, and they may or may not ever tell you so.
within a
million miles of an event like that. No wonder the God-fearing folks >>>>> reckon the world's going to hell in a handbasket. :(
What does god have to do with such a procession?
Could always move to places that tolerate that sort of stuff. Saudi
Arabia. Moscow. Abilene, Texas. Lots of options.
But Mr. Larkin seems to prefer it in San Fran and you seem to prefer
flitting about western Europe, interesting.
Well, I did warn John about moving to SF many years ago as I could tell >>>the way it was going, but he went ahead anyway and seems to have an >>>uncanny ability to only notice the nice side of the place (mainly by not >>>venturing downtown, it seems).
I've only been to SF for a 1 week visit but I can think of no reason why I wouldn't live there if I had sufficient income and a
place to live (which seems unlikely).
From what John has said it sounds like SF is a very tolerant place which would be a plus with me.
"john larkin" <jlarkin_highland_tech> wrote in message news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's >>>>>> a good day to stay close to home. Traffic and parking and
everything will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God
almighty!
I've never seen such a complete and utter freak show in my entire
life.
I just stood there gaping open-mouthed at the procession.
Why were you at the procession? Why did you not stay at home or away
from the procession?
Or was it that the procession passed your home?
It must have been pretty obvious to any of those weirdos on the
floats that I wasn't there to celebrate them!
Why would that have been obvious to them?
I just find it bizarre that parents actually take their kids to see
this sort of thing and they're all waving their rainbow flags and
whatnot.
No kids of mine would be allowed
You could find that they remember you for that, and they may or may not
ever tell you so.
within a million miles of an event like that. No wonder the
God-fearing folks reckon the world's going to hell in a handbasket.
:(
What does god have to do with such a procession?
Could always move to places that tolerate that sort of stuff. Saudi
Arabia. Moscow. Abilene, Texas. Lots of options.
But Mr. Larkin seems to prefer it in San Fran and you seem to prefer
flitting about western Europe, interesting.
Well, I did warn John about moving to SF many years ago as I could tell >>>the way it was going, but he went ahead anyway and seems to have an >>>uncanny ability to only notice the nice side of the place (mainly by
not venturing downtown, it seems).
I've only been to SF for a 1 week visit but I can think of no reason why
I wouldn't live there if I had sufficient income and a place to live
(which seems unlikely).
From what John has said it sounds like SF is a very tolerant place which would be a plus with me.
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's >>>>>>> a good day to stay close to home. Traffic and parking and
everything will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God
almighty!
I've never seen such a complete and utter freak show in my entire
life.
I just stood there gaping open-mouthed at the procession.
Why were you at the procession? Why did you not stay at home or away
from the procession?
Or was it that the procession passed your home?
It was an 8 minute walk to the procession and I'd never seen one before.
I'd expected something a bit more dignified.
It must have been pretty obvious to any of those weirdos on the
floats that I wasn't there to celebrate them!
Why would that have been obvious to them?
I can't disguise my expression.
I just find it bizarre that parents actually take their kids to see >>>>>> this sort of thing and they're all waving their rainbow flags and
whatnot.
No kids of mine would be allowed
You could find that they remember you for that, and they may or may not
ever tell you so.
They'd be most grateful. That display was not fit for children to witness.
within a million miles of an event like that. No wonder the
God-fearing folks reckon the world's going to hell in a handbasket. >>>>>> :(
What does god have to do with such a procession?
Leviticus, I believe. 'Man shall not lay with man nor woman lay with
woman' IIRC.
Could always move to places that tolerate that sort of stuff. Saudi >>>>> Arabia. Moscow. Abilene, Texas. Lots of options.
But Mr. Larkin seems to prefer it in San Fran and you seem to prefer >>>>> flitting about western Europe, interesting.
Well, I did warn John about moving to SF many years ago as I could tell >>>>the way it was going, but he went ahead anyway and seems to have an >>>>uncanny ability to only notice the nice side of the place (mainly by >>>>not venturing downtown, it seems).
I've only been to SF for a 1 week visit but I can think of no reason why
I wouldn't live there if I had sufficient income and a place to live
(which seems unlikely).
From what John has said it sounds like SF is a very tolerant place which
would be a plus with me.
If you're gay, that's fine by me. What I cannot understand is why these >processions are purposely - it seems to me - so outrageously offensive to >normal people. They don't have to be. Why are they? Why do these people go >out of their way to stultify their own cause? It makes no sense to me at
all. I can't possibly celebrate behaviour like that.
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's >>>>>>> a good day to stay close to home. Traffic and parking and
everything will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God
almighty!
I've never seen such a complete and utter freak show in my entire
life.
I just stood there gaping open-mouthed at the procession.
Why were you at the procession? Why did you not stay at home or away
from the procession?
Or was it that the procession passed your home?
It was an 8 minute walk to the procession and I'd never seen one before.
I'd expected something a bit more dignified.
It must have been pretty obvious to any of those weirdos on the
floats that I wasn't there to celebrate them!
Why would that have been obvious to them?
I can't disguise my expression.
I just find it bizarre that parents actually take their kids to see >>>>>> this sort of thing and they're all waving their rainbow flags and
whatnot.
No kids of mine would be allowed
You could find that they remember you for that, and they may or may not
ever tell you so.
They'd be most grateful.
That display was not fit for children to witness.
within a million miles of an event like that. No wonder the
God-fearing folks reckon the world's going to hell in a handbasket. >>>>>> :(
What does god have to do with such a procession?
Leviticus, I believe. 'Man shall not lay with man nor woman lay with
woman' IIRC.
Could always move to places that tolerate that sort of stuff. Saudi >>>>> Arabia. Moscow. Abilene, Texas. Lots of options.
But Mr. Larkin seems to prefer it in San Fran and you seem to prefer >>>>> flitting about western Europe, interesting.
Well, I did warn John about moving to SF many years ago as I could tell >>>>the way it was going, but he went ahead anyway and seems to have an >>>>uncanny ability to only notice the nice side of the place (mainly by >>>>not venturing downtown, it seems).
I've only been to SF for a 1 week visit but I can think of no reason why
I wouldn't live there if I had sufficient income and a place to live
(which seems unlikely).
From what John has said it sounds like SF is a very tolerant place which
would be a plus with me.
If you're gay, that's fine by me.
What I cannot understand is why these
processions are purposely - it seems to me - so outrageously offensive to
normal people.
They don't have to be. Why are they? Why do these people go
out of their way to stultify their own cause? It makes no sense to me at
all. I can't possibly celebrate behaviour like that.
On Mon, 8 Jul 2024 19:59:41 -0000 (UTC), Cursitor Doom <cd999666@notformail.com> wrote:
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's >>>>>>>> a good day to stay close to home. Traffic and parking and
everything will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God
almighty!
I've never seen such a complete and utter freak show in my entire >>>>>>> life.
I just stood there gaping open-mouthed at the procession.
Part of our religious and (former) legal condemnation of extra-marital
and gay sex probably evolved to preventing transmitting diseases.
"john larkin" <jlarkin_highland_tech> wrote in message news:k2jo8jphf5vp8b14apec2sau1msuo3q3lv@4ax.com...
On Mon, 8 Jul 2024 19:59:41 -0000 (UTC), Cursitor Doom
<cd999666@notformail.com> wrote:
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's >>>>>>>>> a good day to stay close to home. Traffic and parking and
everything will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>>>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God
almighty!
I've never seen such a complete and utter freak show in my entire >>>>>>>> life.
I just stood there gaping open-mouthed at the procession.
Part of our religious and (former) legal condemnation of extra-marital
and gay sex probably evolved to preventing transmitting diseases.
Ah someone making logical sense instead of expecting an irrelevant law, written 2000 years or so before English even existed, to be
in any way relevant to here and now.
That's refreshing.
On Mon, 8 Jul 2024 17:12:42 -0400, "Edward Rawde"
<invalid@invalid.invalid> wrote:
"john larkin" <jlarkin_highland_tech> wrote in message news:k2jo8jphf5vp8b14apec2sau1msuo3q3lv@4ax.com...
On Mon, 8 Jul 2024 19:59:41 -0000 (UTC), Cursitor Doom
<cd999666@notformail.com> wrote:
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's >>>>>>>>>> a good day to stay close to home. Traffic and parking and
everything will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>>>>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God >>>>>>>>> almighty!
I've never seen such a complete and utter freak show in my entire >>>>>>>>> life.
I just stood there gaping open-mouthed at the procession.
Part of our religious and (former) legal condemnation of extra-marital
and gay sex probably evolved to preventing transmitting diseases.
Ah someone making logical sense instead of expecting an irrelevant law, written 2000 years or so before English even existed, to be
in any way relevant to here and now.
The Ten Commandments still make sense. They work.
That's refreshing.
Social evolution probably becomes genetic evolution. They go together.
One thing I have noted about gay guys is that they tend to be
promiscuous, wildly so, even married ones. My theory is that women
have some chemicals that are deeply satisfying and make us fall
asleep. The first AIDS cases here were among people who had had
something like 3000 sexual partners. The mind boggles.
This is a great book:
<https://www.amazon.com/Band-Played-Politics-Epidemic-20th-Anniversary/dp/0312374631>
Randy wrote it as he was dying of AIDS.
On Mon, 8 Jul 2024 17:12:42 -0400, "Edward Rawde"
<invalid@invalid.invalid> wrote:
"john larkin" <jlarkin_highland_tech> wrote in message news:k2jo8jphf5vp8b14apec2sau1msuo3q3lv@4ax.com...
On Mon, 8 Jul 2024 19:59:41 -0000 (UTC), Cursitor Doom
<cd999666@notformail.com> wrote:
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so it's >>>>>>>>>> a good day to stay close to home. Traffic and parking and
everything will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>>>>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God >>>>>>>>> almighty!
I've never seen such a complete and utter freak show in my entire >>>>>>>>> life.
I just stood there gaping open-mouthed at the procession.
Part of our religious and (former) legal condemnation of extra-marital
and gay sex probably evolved to preventing transmitting diseases.
Ah someone making logical sense instead of expecting an irrelevant law, written 2000 years or so before English even existed, to
be
in any way relevant to here and now.
The Ten Commandments still make sense. They work.
That's refreshing.
Social evolution probably becomes genetic evolution. They go together.
One thing I have noted about gay guys is that they tend to be
promiscuous, wildly so, even married ones.
My theory is that women
have some chemicals that are deeply satisfying and make us fall
asleep. The first AIDS cases here were among people who had had
something like 3000 sexual partners. The mind boggles.
This is a great book:
https://www.amazon.com/Band-Played-Politics-Epidemic-20th-Anniversary/dp/0312374631
Randy wrote it as he was dying of AIDS.
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
If you're gay, that's fine by me. What I cannot understand is why these processions are purposely - it seems to me - so outrageously offensive to normal people. They don't have to be. Why are they?
Why do these people go out of their way to stultify their own cause?
The Ten Commandments still make sense. They work.
On 7/9/24 01:04, john larkin wrote:
[...]
The Ten Commandments still make sense. They work.
The first three are just job protection. The last six
can be summarized as "Don't do to others what you don't
want them to do to you." There. Just two will suffice.
Jeroen Belleman
On Tue, 9 Jul 2024 10:21:39 +0200, Jeroen Belleman
<jeroen@nospam.please> wrote:
On 7/9/24 01:04, john larkin wrote:
[...]
The Ten Commandments still make sense. They work.
The first three are just job protection. The last six
can be summarized as "Don't do to others what you don't
want them to do to you." There. Just two will suffice.
Jeroen Belleman
I think that the commandments were the first steps of the Enlightment,
which has a way to go still.
Islam and communism are steps in the wrong direction.
"Don't do to others" has its own problems. For starters, individuals
will have different opinions about what's OK. Rape and bank robbery
should be illegal for everyone.
On Sun, 30 Jun 2024 11:57:21 +0100, piglet <erichpwagner@hotmail.com>
wrote:
Thanks, Erich. I did wonder if radians had something to do with it.
However, knowing that 2 pi radians = 360 degrees or a full wavelength
doesn't help me understand why this figure multiplied by the frequency multiplied by the inductance gives us the reactance of a coil. Small
omega therefore equals one second's worth of signal and I don't get
how multipying that by the inductance amounts to the reactance!
On 2024-06-30, Cursitor Doom <cd@notformail.com> wrote:
On Sun, 30 Jun 2024 11:57:21 +0100, piglet <erichpwagner@hotmail.com>
wrote:
Thanks, Erich. I did wonder if radians had something to do with it.
However, knowing that 2 pi radians = 360 degrees or a full wavelength
doesn't help me understand why this figure multiplied by the frequency
multiplied by the inductance gives us the reactance of a coil. Small
omega therefore equals one second's worth of signal and I don't get how
multipying that by the inductance amounts to the reactance!
Something abourt e to the power of sqrt(-1) times theta
"Cursitor Doom" <cd999666@notformail.com> wrote in message news:v6hgfc$10h93$3@dont-email.me...
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom...
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
Gentlemen,
rlkey=n4xinzzm39bms9w04syb7egkx&raw=1
Today is San Francisco Pride Day (Dikes on Bikes and such) so
it's a good day to stay close to home. Traffic and parking and >>>>>>>> everything will be a nightmare.
https://sfpride.org/parade
https://www.dropbox.com/scl/fi/j698pjo7jxm152zuzu4dx/ >>>>>Pink_Triangle.jpg?
I went to one of those once in Berlin when I lived there. God
almighty!
I've never seen such a complete and utter freak show in my entire >>>>>>> life.
I just stood there gaping open-mouthed at the procession.
Why were you at the procession? Why did you not stay at home or away
from the procession?
Or was it that the procession passed your home?
It was an 8 minute walk to the procession and I'd never seen one
before.
So you made a deliberate decision to attend.
I'd expected something a bit more dignified.
It must have been pretty obvious to any of those weirdos on the
floats that I wasn't there to celebrate them!
Why would that have been obvious to them?
I can't disguise my expression.
I don't think they would have cared.
I just find it bizarre that parents actually take their kids to
see this sort of thing and they're all waving their rainbow flags >>>>>>> and whatnot.
No kids of mine would be allowed
You could find that they remember you for that, and they may or may
not ever tell you so.
They'd be most grateful.
How do you know this? Are they allowed to think for themselves?
That display was not fit for children to witness.
within a million miles of an event like that. No wonder the
God-fearing folks reckon the world's going to hell in a
handbasket.
:(
What does god have to do with such a procession?
Leviticus, I believe. 'Man shall not lay with man nor woman lay with
woman' IIRC.
Oh dear.
Could always move to places that tolerate that sort of stuff.
Saudi Arabia. Moscow. Abilene, Texas. Lots of options.
But Mr. Larkin seems to prefer it in San Fran and you seem to
prefer flitting about western Europe, interesting.
Well, I did warn John about moving to SF many years ago as I could >>>>>tell the way it was going, but he went ahead anyway and seems to have >>>>>an uncanny ability to only notice the nice side of the place (mainly >>>>>by not venturing downtown, it seems).
I've only been to SF for a 1 week visit but I can think of no reason
why I wouldn't live there if I had sufficient income and a place to
live (which seems unlikely).
From what John has said it sounds like SF is a very tolerant place
which would be a plus with me.
If you're gay, that's fine by me.
LOL when did I give any indication of my sexuality? LOL Ok maybe you
meant 'you' in the plural sense but still LOL
What I cannot understand is why these processions are purposely - it
seems to me - so outrageously offensive to
normal people.b
What distinguishes a normal person from one who is not normal?
They don't have to be. Why are they? Why do these people go out of
their way to stultify their own cause? It makes no sense to me at all.
I can't possibly celebrate behaviour like that.
You don't have to deliberately attend either.
On Mon, 8 Jul 2024 17:05:09 -0400, Edward Rawde wrote:....
"Cursitor Doom" <cd999666@notformail.com> wrote in message
news:v6hgfc$10h93$3@dont-email.me...
On Mon, 8 Jul 2024 14:08:33 -0400, Edward Rawde wrote:
"john larkin" <jlarkin_highland_tech> wrote in message
news:bge68jhpanmo6vs4j780am19vc6fh9ndfo@4ax.com...
On Mon, 1 Jul 2024 17:49:00 -0000 (UTC), Cursitor Doom
<cd999666@notformail.com> wrote:
On Mon, 1 Jul 2024 13:39:51 -0400, bitrex wrote:
On 6/30/2024 12:45 PM, Cursitor Doom wrote:
On Sun, 30 Jun 2024 07:38:19 -0700, john larkin wrote:
On Sun, 30 Jun 2024 14:23:24 +0100, Cursitor Doom
<cd@notformail.com>
wrote:
On Sun, 30 Jun 2024 06:05:41 -0700, john larkin
<jlarkin_highland_tech> wrote:
On Sun, 30 Jun 2024 08:44:34 +0100, Cursitor Doom
<cd@notformail.com> wrote:
I only went out of curiosity. Never seen one before.
And I'll never watch another one. A re-enactment of a Bacchanalian orgie
is not the kind of entertainment I like to see
and is 100% NOT suitable
for children. Anyone who takes a child to see an event like that needs to have the child taken away and fostered to a loving heterosexual couple who will bring it up properly.
On Wed, 10 Jul 2024 07:47:29 -0000 (UTC), Jasen Betts wrote:
On 2024-06-30, Cursitor Doom <cd@notformail.com> wrote:
On Sun, 30 Jun 2024 11:57:21 +0100, piglet <erichpwagner@hotmail.com>
wrote:
Thanks, Erich. I did wonder if radians had something to do with it.
However, knowing that 2 pi radians = 360 degrees or a full wavelength
doesn't help me understand why this figure multiplied by the frequency
multiplied by the inductance gives us the reactance of a coil. Small
omega therefore equals one second's worth of signal and I don't get how
multipying that by the inductance amounts to the reactance!
Something abourt e to the power of sqrt(-1) times theta
Well this is something else that's new to me. I only just encountered it
last month when reading Tom Lee's book 'Planar Microwave Engineering' in which he uses some very unfamiliar (to me) mathematics. I was going to
post a question about it here in fact. Mebe I'll get around to it if time permits...
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