Hello TK
I'll answer you objections in full - later tonight.  I've been dying to get my teeth into that post of yours.  Right now I'm busy.  But nice to see you're concerned.

Rosie Pose

 

@PW: Sure, I see exactly where you are going. My bulbs aren't quite _that_ dim !.....   

But today I'm going outside and setting up the TinselScope to take a look at old Sol. It's beautifully clear and might be so tonight as well. I've been missing some observing time at night because of all this present nonsense but if it's clear tonight I hope to get this season's first glimpse (for me) of Saturn. Mars, too, is presenting beautifully right now but is heading westward and will be setting earlier and earlier. The idiot city has started leaving lights on all night at the tennis courts at the park two blocks north.... and that kills my best galaxy viewing. I don't know how it will affect astrophotography yet... perhaps we'll see tonight if it stays clear and dry.

Stay tuned... when Rosemary wakes up there will be a lot more bold red stuff coming "with respect".

BTW.... has your "slow boat" full of mosfets arrived yet?

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 assume 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 analyze 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 dissipaters 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 (using the Wattage probe) 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 (which used the VCSR(t) x VBAT(t)) 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.

For this next installment, let’s begin by reviewing one of the last simulation test runs. Referring to
schema07.png and the associated scope shot scope13.png, we see that when the oscilloscope
probes are placed directly across the terminals of one of the six batteries, the scope trace is
essentially a flat line at the 12V level, indicating the battery’s DC voltage reading. Providing that
the battery’s internal resistance is reasonably low (typically less than 0.01 Ohms when fully
charged), the scope trace will be reasonably, if not perfectly flat, with no ripple caused by the
circulating currents. In practice however, there will always be a finite internal resistance, and at
times when the battery is not fully charged, we may in fact see some small amount of ripple riding
on the flat 12V trace. Depending on the currents being drawn from the battery and the battery’s
state of charge (SOC), the amount of ripple might vary from a few millivolts, to several hundred
millivolts. In most cases, the ripple won’t exceed 1Vp or so.

Generally speaking however, when measuring the battery voltage on a loaded but charged
battery, the resulting trace will essentially be a flat line at the voltage level present directly on
the battery terminals. For all intents and purposes, this voltage is “pure DC”, and will be referred
to as “DC” from this point forward.

Reviewing the methodology involved in obtaining the measurement of average input power (Pin),
we have:

Pin(avg) = AVG[VBAT(t) x VCSR/CSR(t)], or in words;

Average input power is equal to the average of the product of the instantaneous battery voltage,
and the scaled (by the CSR value) instantaneous voltage across the CSR.

For the moment, we will acknowledge that the CSR value will vary (due to the presence of 200nH
of parasitic inductance in series with the CSR, as shown) under the conditions of a high
frequency current through it.

Knowing that a properly measured battery voltage will result in essentially a flat DC trace, we can
slightly alter the above power equation to the following:

Pin(avg) = AVG[VBAT(DC) x VCSR/CSR(t)], or in words;

Average input power is equal to the average of the product of the battery voltage (in DC), and the
scaled (by the CSR value) instantaneous voltage across the CSR.

From this we can see that the DC battery voltage is simply a constant multiplying factor that is
applied to the VCSR/CSR(t) factor in the power equation. There are no phase considerations
involved here because the phase angle between a DC voltage and any current (varying or not) is
0º. The COS of 0º is 1, and this means that the power factor associated with a DC source is 1. So
although still valid, it should now be obvious that an oscilloscope channel is NOT required to
properly obtain the required battery voltage for a DC INPUT power measurement! A digital
voltage meter (DVM, DMM) placed directly across the battery terminals is all that is
needed.

What if we don’t measure the battery voltage with the probes placed directly across the battery
terminals? Well, it turns out that if dealt with properly, this is not a huge problem at all. We know
that the battery voltage should be essentially a flat line representing the battery terminal voltage.
We also know that if we take a battery voltage measurement with the probes placed across two
points that include any amount of parasitic inductance (i.e. battery wiring), the measurement
points will show a considerable amount of ripple riding on the true DC voltage if observed with an
oscilloscope. No problem.

Because we know that the battery voltage should be “flat”, we are permitted to apply a significant
amount of filtering (or averaging) to the signal being measured across these two “displaced”battery measurement points. The result is a reading of DC voltage minus a small DC voltage drop
across the battery wiring resistance. In other words, this voltage measurement will be extremely
close to the same measurement made with the probes directly across the battery terminals.
Let’s look at this scenario with the simulation, and see how close the two measurements are:
Referring to schema01.png, note the green probe at measurement point 7 (ignore the CSR
probes for now). scope16.png shows the battery voltage as measured from nodes 7 to 4 (GND).
The peak to peak voltage is over 200Vpp, but after averaging, the value is a little under 71VDC.
The averaging is done with the built-in function in PSpice, however the same result is achieved by
measuring the same points with a DMM, with or without the utilization of a non-intrusive RC filter
in front of it. The six 12V batteries add to 72VDC, but some voltage drop is expected due to the
wiring resistance of 2 Ohms total.

So it has now been established that you can obtain a clean accurate battery voltage
measurement as part of the INPUT power measurement, by using a DVM and non-loading RC
filter (optional). Moreover, the battery voltage measurement can also be obtained using an
oscilloscope channel by applying a running MEAN function to the resulting trace, and as long as
averaging is performed on this measurement, the measurement probes do not have to be placed
directly on the battery terminals. This applies to both a scope and DMM measurement.