# S.C battery in AC analysis

Discussion in 'General Electronics Chat' started by youngprof, Jul 2, 2012.

1. ### youngprof Thread Starter New Member

Jul 2, 2012
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0
i`m wondering if anyone could tell me, why we make the DC battery in AC Analysis as a Short Circuit so collector of BJT pulled down to ground, and so for a BJT biased circuit if we have a collector resistor Rc and a Load one RL , they will be in parallel, so if we give an AC voltage input on base, the two resistors becomes parallel while in DC analysis without putting AC voltage into consideration there is no matching or parallel effect between them . Why?!!

2. ### wmodavis Well-Known Member

Oct 23, 2010
737
149
Because the ac impedance of an ideal power supply or DC battery is zero.

In reality they are not quite zero but close enough such that the PS actual impedance is much less then other circuit impedances and so zero is a good approximation.

3. ### crutschow Expert

Mar 14, 2008
12,573
3,082
Because the two analyses are entirely different. For DC analysis we are determining the bias conditions of the circuit DC power paths from power supply to ground, whereas for AC analysis we are determining the operating parameters of the AC signal path from input to output. Those two pathways are very different, thus the parameters we calculate for the analyses are different.

4. ### WBahn Moderator

Mar 31, 2012
17,459
4,701
It is because the analysis you are talking about is nothing more than analysis via superposition, meaning that the circuit is analyzed more than one, but each supply is turned on in exactly one of the analyses. Then the total response is the sum of all of the responses.

If you had a linear circuit that has, say, a DC source and two AC sources at different frequencies, you would do the analysis three times, one for each source with the impedance of the components evaluated at that source's frequency (i.e., 0 for DC).

If you have a transistor circuit, the the same idea is being used, but with a slight-of-hand to deal with the nonlinear nature of the transistors and diodes and such. So we once again split the analysis into two pieces. In one we turn on all, but only, the DC sources and solve the circuit under those conditions. We call this the "DC", the "bias", or the "large-signal" response. Then, we replace the nonlinear components with linear models that are reasonably good as long as the signals aren't too large (with "too large" being signals that result in our model no longer being "reasonably good"). We call this the "small-signal" response, even though the signals are not always what we might call "small". We then analyze the circuit again with only the non-DC sources turned on. As before, the total response is the sum of the two, the frequently we only care about the nature of the small-signal response (but, if you are actually building the thing, you can't ignore the DC response).

So, with this in mind, imagine a circuit that has +12V and -12V supplies and nothing but two resistors in series going from +12V to =12V. Call the junction between the two resistors Node A. Now connect Node A to Node B, which is the output of a sinusoidal voltage signal. The DC response will have 24V across the two resistors and come up with some voltage at Node A via a voltage divider. There will be no contribution from the sinusoidal source both because it is turned off, but more importantly because the capacitor looks like a short-circuit at DC. Now do the small-signal response by turning off the two DC sources. This puts the the two far ends of the resistors both at 0V and, since the other ends are both connected to Node A, they are in parallel. We now have a series RC circuit driven by our sinusoidal source. We analyze it and get the signal at Node A from that source. The complete voltage at Node A is then the sum of the DC bias point and the sinusoidal small-signal.