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Next: Emitter Follower Up: ch4 Previous: Small Signal Model and

AC equivalent circuits

As discussed before, the voltage a circuit receives from a source depends on its input impedance $R_{in}$ as well as the internal impedance $R_s$ of the source, while the voltage it delivers depends on its output impedance $R_{out}$ as well as the load impedance $R_L$. It is therefore important to consider these input and output impedances of an amplification circuit as well as its voltage gain.

AmplifierSourceLoad.gif

In the first figure, everything inside the red box, including the amplifier as well as $V_S$ and $R_s$, is treated as the source, while everything inside the blue box, including the amplifier as well as $R_L$, is treated as the load. Given the amplifier as well as the source $V_S$ and $R_s$, and the load $R_L$, we need to find the following three parameters so that the red and blue boxes in the first figure can be modeled by the corresponding boxes in the second figure:

Consider the typical transistor AC amplification circuit below:

ACamplification1.gif

If the capacitances of the coupling capacitors and the emitter by-pass capacitor are large enough with respect to the frequency of the AC signal in the circuit is high enough, these capacitors can all be approximated as short circuit. Moreover, note that the AC voltage of the voltage supply $V_{CC}$ is zero, it can be treated the same as the ground. Now the AC behavior of the transistor amplification circuit can be modeled by the following small signal equivalent circuit:

ACamplification2a.gif

ACamplifierModel.gif

As shown above, this AC small signal equivalent circuit can be modeled by as an active circuit containing three components:

Example:

DCACloadlineEx.gif

Here $V_{CC}=12V$, $R_B=300 k\Omega$, $R_C=R_L=4 k\Omega$, and $\beta=40$. We also assume $R_s=0$, and the capacitances are large enough so that they can be considered as short circuit for AC signals.

DCACloadline.gif transistorBJTexample1c.gif

The circuit above can also be analyzed using the small-signal model.

DCACloadlineExModel.gif

Same as before, $r_{be}=1  k\Omega$, and we have the following DC variables:

\begin{displaymath}
I_B=(V_{CC}-V_{BE})/R_B \approx V_{CC}/R_B=40 \;\mu A
\end{displaymath}


\begin{displaymath}
I_C=\beta\;I_B=40\times 40\;\mu A=1.6\;mA
\end{displaymath}


\begin{displaymath}
V_{CE}=V_{CC}-R_C I_C=12-1.6\times 4=5.6\;V
\end{displaymath}

The AC variables:

\begin{displaymath}
i_b=v_{in}/r_{be}, \;\;\;\;v_c=-i_c\; (R_C\vert\vert R_L)
\end{displaymath}

The voltage gain is:

\begin{displaymath}
A_v=\frac{v_c}{v_{in}}=-\frac{\beta\; i_b\;(R_C\vert\vert R_...
... R_L)}{r_{be}}
=-\frac{(40\times 2)\;k\Omega}{1\;k\Omega}=-80
\end{displaymath}

The input resistance is $R_{in}=R_B\vert\vert r_{be}\approx r_{be}=1 k\Omega$, the output resistance is $R_{out}=R_C=4\;k\Omega$.


next up previous
Next: Emitter Follower Up: ch4 Previous: Small Signal Model and
Ruye Wang 2016-07-25