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Active Components and Circuits

All circuits we have discussed so far are only composed of passive components (resistors, capacitors and inductors) driven by current and/or voltage sources. Later we will consider circuits containing active components such as bipolar junction transistors (BJT), field-effect transistors (FET), operational amplifiers (Op-Amps) containing many transistors, and voltage amplifiers. These active components can be considered as controlled voltage or current sources as functions (typically linear) of the input voltage or current.

Example 3:


Find $R_{in}$, $R_{out}$, and $A_{oc}$ of this two-port network containing $R_1$ and $R_2$ as well as the amplifier modeled by $r_{in}$, $r_{out}$ and $A$.

This 2-port network modeled as a voltage amplifier with $R_{in}$, $R_{out}$ and $A_{oc}$ can be used in more complicated circuits.

Example 4:

A 2-port network with a voltage aplifier on the left can be modeled by the circuit on the right. Find the parameters $R_{in}$, $R_{out}$ and $A_{oc}$ of the two-port network with the voltage amplifier embedded.


In summary, the resistor $R_1$ shared by both the input and output loops serves as a negative feedback:

\begin{displaymath}v_s\uparrow \rightarrow i_{in}, v_{out}\uparrow \rightarrow v_1\uparrow
\rightarrow i_{in}, v_{out}\downarrow \end{displaymath}

As the result, the voltage gain $A_{oc}$ is reduced but both the input and output resistances are improved, i.e., $R_{in}$ is increased and the $R_{out}$ is reduced.

Example 5: (Homework)


A voltage amplifier, denoted by the inner box (solid line) with three internal parameters $r_{in}$, $r_{out}$ and $A$, is used as a component in a two-port network, denoted by the outer box (dashed line). Its open-circuit output voltage is $Av_{in}$. Find the following three parameters of the two-port network.

Note that all output $v_{out}$ between C and D of the output port is fed back to the input port between A and B: $v_s=v_{in}+v_{out}$ or $v_{in}=v_s-v_{out}$, i.e., it is a negative feedback.

Then simplify the three results above by making reasonable approximations based on the assumptions that $A»1$, $r_{in}»r_{out}$.


Example 6: (Homework)


Two amplifiers with parameters $A_1$, $r_{i1}$, $r_{o1}$ and $A_2$, $r_{i2}$, $r_{o2}$, respectively, can be connected in cascade as shown in the figure. Given a voltage source $v_s$ in series with an internal resistance $R_s$, find the output voltage. To maximize the output $v_{out}$, how would you change the values of the six parameters?

Find the power gain $G_p$ of the system.


Example 7: (Homework)

The input and output resistances $R_{in}$ and $R_{out}$, as well as the voltage gain $A_{oc}$ of a two-port network can be obtained experimentally. First, connect an ideal voltage source $v_s$ (a new battery with very low internal resistance) in series with a resistor $R_s$, and then connect load $R_L$ of two different resistances to the output port. Now the three parameters can be derived from the known values of $v_s$, $R_s$ and the two measurements of the load voltage $v_{out}$, corresponding to the two resistance values used.

Assume $v_s=1.5V$, $R_s=5 k\Omega$, and the input voltage is measured to be $v_{in}=1.25 V$; also, assume the two different load resistors used are $R_1=150 \Omega$ and $R_2=200 \Omega$ respectively, with the two corresponding output voltage $v_1=18.75V$ and $v_2=20$. Find $R_{in}$, $R_{out}$ and $A_{oc}$.


next up previous
Next: About this document ... Up: Chapter 2: Circuit Principles Previous: Two-Port Networks
Ruye Wang 2017-07-03