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For the next installment of simulation test runs, it's necessary to establish some simple background theory:
If each of the 6 twelve-volt batteries in the battery array have approximately the same state of charge, terminal voltage, and internal resistance, it is reasonable to asssume that each of the 6 batteries will receive or supply the same amount of power in the circuit. As such, it is valid to measure and analyse the power in any one of the 6 batteries and apply a factor of 6x to obtain the total power in the circuit.
In this first test, the battery voltage probes are placed across the last jumper wire and last 12V battery. So we are measuring the voltage across a single 12V battery in series with 400nH of wire inductance in a single jumper. The power computes to -3.8W.
Next, when the battery voltage probes are placed directly across the single 12V battery and no jumper, the power changes polarity and computes to roughly +1.4W.
When the wattage probe available in PSpice is used to directly measure the instantaneous power of the single 12V battery, it computes to a net average of approximately -5.45W. If you recall the exercise on the polarity of power sources vs. power dissipators a little while back, you will know that the proper polarity for a source that is sourcing power, is negative. The reason the last computation of +1.4W turned out positive, is because the voltage probes across the CSR are reversed (as a matter of establishing common ground for both the CSR and battery probes). This has been the case throughout this exercise. It adds a bit of confusion, but that is the direction the "powers" normally go and it's important to keep this straight in one's mind.
Now back to the issue of the correct value for the CSR. As we now know the true power in any one of the six 12V batteries is about -5.45W, and that the previous measurement using a single 12V battery times the CSR voltage (battery current) came to approximately +1.4W (assuming a 1 Ohm value for the CSR), it may become obvious that assuming the CSR value to be anything other than 0.25 Ohms is incorrect. If we take the +1.4W measurement and multiply it by 4x (1/0.25), we obtain a power of about +5.6W. I have been approximating the values read off the scope, so in reality the previous measurement would actually be closer to 1.37W. It should be clear from this that the correct value for the CSR when looking at DC INPUT power, is the actual resistive value of the CSR, in this case 0.25 Ohms (regardless if the current is pulsed at a high frequency or not).
Computing the total power from all 6 batteries in the array we have:
-5.45W x 6 = -32.7W
This is the actual correct value and polarity for the total INPUT power of the battery array in this particular simulation.
Now, if we take the previous +1.37W measurement using just a single battery and no jumper wire, and multiply it by 4 (because of the 0.25 Ohm CSR), then by 6 (for 6 batteries in the array), we obtain a power of about +32.88W.
Other than the polarity difference (because the CSR probes are reversed), the two powers are almost identical in magnitude, and it is safe to say that now with the inductance eliminated in the battery voltage measurement, the VCSR(t) x VBAT(t) computation by the scope is very accurate.
All schematics and scope shots attached. More to follow.
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"Some scientists claim that hydrogen, because it is so plentiful, is the basic building block of the universe. I dispute that. I say there is more stupidity than hydrogen, and that is the basic building block of the universe." Frank Zappa
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Topic: The Rosemary Ainslie Circuit (Read 460400 times)
