  24 February 2009
Author: Giorgos Lazaridis
BJT Transistor theory

DC and AC equivalents

As we said previously, a transistor amplifier usually operates both with AC and DC voltages, the DC voltage is used to bias the transistor and the AC voltage is the signal that will be amplified. To analyze a transistor circuit, both voltages must be analyzed. But the transistor itself as well as the biasing components react differently in AC and DC signals. Obviously, there must be a method to analyze each signal separately. The simplest and most widely used method is using the DC and AC equivalents. According to this method, two equivalent circuits are extracted from the original circuit, the DC and the AC equivalent. The currents and voltages for each circuit are calculated separately, and then, using the superposition theorem we can calculate the final values. For your information, the superposition theorem states that:

"The response -voltage or current- in any branch of a bilateral linear circuit having more than one independent source, equals the algebraic sum of the responses caused by each independent source acting alone, while all other independent sources are replaced by their internal impedances."

Making the DC equivalent

To make the DC equivalent circuit, the following steps must be taken:

• I] All AC sources become zero.
• II] All capacitor are replaced with an open circuit

• Suppose for example that we have the following circuit from which we want to make the DC equivalent: According to the first rule, all AC sources (if any) must become zero. This applies for the "Input" AC source that we have. When a power source becomes zero, it means that the output voltage will always have the same potential as the grounding signal - which is zero. Therefore we replace it with a grounding signal. According to the second rule, all capacitors must be replaced with an open circuit. CIN must be replaced with an open circuit, thus the Input AC supply can be omitted. COUT is also replaced with an open circuit, thus RL can be omitted. Here is the resulting DC equivalent circuit: The above circuit can be simplified: Having this circuit, it is very simple to make the DC analysis, since there is no AC source whatsoever. From this analysis, the designer is able to calculate all the DC biasing values, draw the DC load line and set the quiescence point.

Making the AC equivalent

To analyze the AC signals, we need to make the AC equivalent circuit. The following steps must be taken:

• I] All DC sources become zero
• II] All capacitors are replaced with a bridge

• When we designed the DC equivalent, we simple removed the AC sources. That is because the AC sources were coupled through decoupling capacitors, and due to the fact that all capacitors were replaced with open circuits, we simple removed the AC sources. But its not the same for the DC equivalent. The DC sources are directly coupled to the circuit so we cannot remove them. Therefore, according to the first step, all DC sources become zero. In other words, every component that is connected to the positive DC supply must be grounded. Then, we replace the capacitors with bridges: The above circuit can be simplified: In many cases (like this one) the resulting circuit can be further simplified. The two resistors of the voltage divider are now connected in parallel, since the top side of RB1 is now grounded. Moreover, the emitter resistor and the load resistor (RE and RL) are also connected in parallel. We can calculate the equivalent resistors for RB1//RB1 and RE//RL and replace them in the circuit: The above circuit is ready for the AC analysis since there is no more a DC source.

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