Hi Richard...
"Richard Harrison" wrote in message
...
[...]
"----Second, it is the RMS current through the tube which will waste
power, so that is what we must be concerned with."
I don`t believe current through a Class C amplifier consists of an
ordinary sine wave.
And I didn't say that it does nor do I believe it does. I'm inclined to
take my 100MHz storage scope to to the 6146's of my TS830s and see for
myself.
Your words imply (at least I infer) you are thinking that only a sine
wave has an RMS value. Every wave of any shape has an effective or RMS
value - its heating or "power causing" value.
[...] I think it consists of short unidirectional pulses.
The tuned "tank circuit" is the source of sine waves.
This certainly has to be correct. The tank will most likely cause some
sine-like VOLTAGE waveform, but the tube current has to be pulses of some
shape. This is a very timely discussion in view of the AC power meter QST
article and the extensive investigation I just completed on several pulse
shapes..
RMS is the effective value, not the average value, of an a-c ampere.
I will differ here. The RMS value is more appropriately described as
the power producing value of ANY wave form. Pulses can produce heat just as
well as sine wave AC. We all know this from a practical view since tubes
can only conduct in one direction and the plates DO get hot.
...as the heating
value of an ampere is proportional to the current squared.
This is actually a simplification. P=ExI Power is the product of
voltage and current *only*. Because this is a second order effect, in a
resistance it can be related to either voltage squared or current squared...
because that captures the second order character. Maybe there's a better way
to say it mathematically, but I don't know it.
When we get to non sine shapes, then we have to fall back on the actual
definition. root [avg of square] ...with the integral and all.
http://www.ultracad.com/rms.pdf
[...snip...]
Ordinarily, with nonsinusoidal currents, the ratio of maximum to
effective value is not the square root of 2.
Best regards, Richard Harrison, KB5WZI
Doing the math for pulses with the shape of sine, triangle (a single
slope with sudden end) and trapezoid (a sudden start to one level then a
slope to a peak and a sudden end), I decided to look at the RMS to AVERAGE
ratio since average is what a common meter will measure in Bob Shrader's
article (AC watt meter Jan 04 QST).
I was particularly interested in the sine-shaped pulses of various duty
cycle because the current of common power supplies occurs in short pulses
with a sine-like shape that are near the peak of the voltage waveform.
It was interesting that for all these shapes, this ratio was very
similar. One relatively simple thing to understand which came out of the
analysis was that the average value is directly proportional to the duty
cycle as you might reasonably postulate. Where duty cycle is the ratio of
"on" time to off time. Where "on" time is the time that ANY current flows.
Whereas the RMS is proportional to the Square root of the duty cycle. e.g.
drop the duty cycle to half and the RMS drops to .707.
I have to do some verification, but it sure looks as though Bob's
numbers can be as much as three times what he quoted, depending on the
waveshape and some measurements I made.
http://www.irf.com/technical-info/an949/append.htm
Trapezoid=rectangular. Also for the phase controlled sine, the things that
look like tau and a small n are both pi i.e. sin [pi x (1-D)] cos [pi x
(1-D)] and denominator of 2 x pi
Some average & RMS values here.
http://home.san.rr.com/nessengr/techdata/rms/rms.html
More (better) average formulas:
http://www.st.com/stonline/books/pdf/docs/3715.pdf
NOW I know where the average value of a sine wave comes from = (2/pi)
The Greek delta = d.
A calculator for RMS:
http://www.geocities.com/CapeCanaveral/Lab/9643/rms.htm