Testing the TK Tar Baby

[poynt99]

Here is an easy method I came up with that will provide an accurate Pout (power in RL) computation:

Pout_AVG = [VCSR(rms)/RCSR]² x RL(hot)

Which means: take the RMS voltage across the CSR, divide it by the CSR value, square it, then multiply it by the resistance value of RL taken when it is at it's equalized hot temperature.

[poynt99]

PW,

It's still further a pity that Greg is ignoring the write-up I posted, and now ignoring me.

I guess it's another case of the typical reaction; when things start looking as though you may be wrong, just bury your head in the sand and hopefully it will all go away. 

[TinselKoala]

Here is an easy method I came up with that will provide an accurate Pout (power in RL) computation:

Pout_AVG = [VCSR(rms)/RCSR]² x RL(hot)

Which means: take the RMS voltage across the CSR, divide it by the CSR value, square it, then multiply it by the resistance value of RL taken when it is at it's equalized hot temperature.

As is also given in the derivation in the image above from the Wiki on "rms". But it states there that this is valid for pure resistive loads. Is there a correction that needs to be applied due to the load's inductive reactance?

[TinselKoala]

Astounding. Let's play math games, shall we.

The frequency = 62,500 Hz,
V = 25.3
RL = 10-Ohms
Duty cycle = 25%

1/(4x62,500) = duration of a single pulse = 0.000004 or 4usec

Here he has taken the frequency of 62.5 kHz, found the inverse to get the period of 16 microseconds, and THEN DIVIDED BY FOUR TO GET THE PULSE "ON" DURATION of 4 microseconds. In other words, he has put the duty cycle in at this point.

25.3V / 10-Ohms = 2.53A
25.3V x 2.53A = 64.009Watts per pulse
64.009watts x 0.000004sec = 0.000256036Watt-sec per pulse

There are 62,500 pulses per second so:
(0.000256036Watt-sec / pulse) x (62,500pulses / sec) = 16.00225Watts
In the latter calculation, I have essentially added up all of the identical packages of instantaneous power, but they are spaced apart over time.

That's right... you have sort of the average power figure here, with the duty cycle already factored in, from the first step. This 16 watts figure is an "average" power, already taking duty cycle into account.
You can get this same answer also by simply taking the voltage times current times duty cycle: 25.3 x 2.53 x 0.25 = 16.00225, or really just 16.0, respecting sig digs.
You have 64 Watts being dissipated for 1/4 second (0.00004 x 62,500 = 0.25) and you have 3/4 seconds off. So for that one second, you have an average power of 64 x 0.25 = 16 Watts. The duty cycle is incorporated in this average power figure already.... to put it in again later is... well, it's either a silly mistake or a deliberate attempt to mislead.

This is NOT continuous power.  For a 25% Duty Cycle, the FET (switch) is closed or "ON" for 25% of the entire pulse period and is open or "OFF" for the remainder of the pulse period or 75%. 

Now this will shock some: The ratio of "ON" times to "OFF" times is:
.25 / .75 = 1/3 even though the ratio of "ON" time to the entire pulse period is .25 (25% Duty Cycle).  My instincts tell me that I should divide the SUM of the Instantaneous powers by '3'.

This latter bit is incredible on its own... dividing by three? .... the "Sum" of the instantaneous powers already is the average power taking the duty cycle into account.  BUT ALSO..... he now applies the duty cycle, or this "one third" bastardization of it, AGAIN.

So, I will do that:
16.00225Watts / 3 = 5.334083Watts
An RMS calculation will yield similar results.

Facepalm. I guess actually dividing by four gave him an answer embarrassingly small, so he had to come up with dividing by three to get something "similar" to the RMS calculation results..... even though he already had the duty cycle in the "sum" of the powers.

So the inductive heater RL breaches the unity barrier likely because of the Oscillations and the EMF recovered by RL's By-Pass Diode.

The above analysis is just about as simple and unambiguous as it gets.

Regards,

Greg

Ah... no, not quite. The conclusion is not justified by the data; the mathematical analysis makes a couple of egregious errors and a totally unjustified "intuition" that tells Greg he should divide by the ratio of on-to-off time, rather than on-to-total-period time as is correct and proper......  for the second time he puts the duty cycle into the calculation, in order to make his new numbers "agree" with his old ones.

And yes, it's hilarious that an rms calculation does yield "similar" results: for a rectangular, positive-going pulse train, Vrms = V x sqrt(dutycycle) and Irms = I x sqrt(dutycycle) so
Vrms x Irms = (25.3 x 0.5) x (2.53 x 0.5) = 16.0. 
QED, this is the average power and duty cycle is already taken into account.

Now... my "instincts" tell me that any further division by, say, four, or three, or any other number is not justified for any reason, unless one is trying to make one's numbers fit some kind of preconceived idea... or "thesis"... without regard to actual fact.

[poynt99]

As is also given in the derivation in the image above from the Wiki on "rms". But it states there that this is valid for pure resistive loads. Is there a correction that needs to be applied due to the load's inductive reactance?

You already have the true rms current. You square that and multiply it by the RL resistance value measured at the equalized temperature. The correction factor is that you are multiplying the squared rms current by the real resistance of the load, i.e. the "RL(hot)" I specified.