![]() In the case of a current source driving the input of a CE amplifier, the current source is “opened”, leaving only its shunted output resistance. If the source element to the input of the CE amplifier is voltage source, then it is “ac-shorted” leaving only its series source resistance to ac-ground. To apply the hybrid-\(\pi\) model to a basic CE amplifier, all circuit elements must be substituted with their small-signal equivalent. The emitter terminal is tied to a common potential or an ac-ground. An ideal capacitor has no series or parallel resistance and is exclusively a reactive element with reactance A detailed explanation of the Laplace transform is beyond the scope of this blog, please consult an alternate reference on the use of the Laplace transform for circuits. Impedance can also be conveniently analyzed in the s-domain (frequency domain). When sinusoidally driven, at steady-state the reactive current is orthogonal to the source voltage and neither generates or expends any net energy. It’s worth emphasizing here that reactance is orthogonalto resistance. Impedance can be applied as a direct substitute for resistance, but the math must be done with complex arithmetic. ![]() For some specific frequency \( \omega = 2\pi f \), impedance is Electrically looking into the terminals of either a Norton or Thévenin equivalent circuit, one could not distinguish between which style was chosen.Įlectrical impedance (\(Z\)) can be applied equivalently to electrical resistance with the inclusion of a complex term \( X\) (reactance). The choice of simplifying a circuit to either a Norton or Thévenin equivalent circuit is completely arbitrary, with the choice typically favouring the one which yields analytical convenience. On the right hand side a current source shunted with a resistor is refereed to as a Norton equivalent circuit. On the left hand side, a voltage source with series resistance is refereed to as a Thévenin equivalent circuit. Here some arbitrary Device Under Test (DUT) or Circuit Under Test (CUT) can be simplified into one of two basic circuits. The figure below depicts this circuit simplification. For any non-linear circuit such as a transistor amplifier, the non-linear behaviour can be linearized about an operating point for small signals. In the case of differential circuits the simplification is made about the positive and negative branches of input/output ports. ![]() ![]() With the second node to chosen as typically being an input or output node for single-ended circuits. One of the most common nodes to be chosen being the circuit common node (typically ground). – High Frequency Model – Grounded Emitterįrom elementary circuit theory, one may recall that any linear circuit may be simplified about two arbitrary circuit nodes. The desired outcome of this post is to gain an intuition into what “it looks like” electrically speaking into the output of a CE amplifier. Concluding the post with a spice simulation to compare/validate the circuit equivalent models developed. A second HF model is developed with a grounded emitter and with source resistance to the input (base) terminal. The first HF model will be for when the base is ac-grounded and the emitter see a degeneration resistor. In this post, a circuit equivalent model of the output impedance of a common-emitter amplifier will be developed. To begin, a low-frequency non-reactive model of the output resistance of a common-emitter (CE) amplifier will be solved. Proceeding models will include the capacitive elements of a CE amplifier. Separating the High-Frequency (HF) model into two distinct cases will allow for circuit analysis that is reasonable to perform by hand. ![]()
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