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 1: Consider the circuit below containing an active component, a voltage amplifier, model by the three parameters , and , dirven by either a current source or a voltage with internal resistance :
The performance of such a circuit containing active components can also be described by terms such as ``voltage gain'' , ``current gain'' , and ``power gain'' , which can be found based on the specific circuits. They are defined as below:
Find , , and of this two-port network containing and as well as the amplifier modeled by , and .
A 2-port network with a voltage aplifier on the left can be modeled by the circuit on the right. Find the parameters , and of the two-port network with the voltage amplifier embedded.
We first find the short-circuit current
at the output port. Assume a voltage source with internal resistance
is applied to the input port while the output port is short-circuited.
Applying KVL to the two loops of the circuit, we get:
Example 5: (Homework)
A voltage amplifier, denoted by the inner box (solid line) with three internal parameters , and , is used as a component in a two-port network, denoted by the outer box (dashed line). Its open-circuit output voltage is . Find the following three parameters of the two-port network.
Note that all output between C and D of the output port is fed back to the input port between A and B: or , i.e., it is a negative feedback.
Then simplify the three results above by making reasonable approximations based on the assumptions that , .
Example 6: (Homework)
Two amplifiers with parameters , , and , , , respectively, can be connected in cascade as shown in the figure. Given a voltage source in series with an internal resistance , find the output voltage. To maximize the output , how would you change the values of the six parameters?
Find the power gain of the system.
Example 7: (Homework)
The input and output resistances and , as well as the voltage gain of a two-port network can be obtained experimentally. First, connect an ideal voltage source (a new battery with very low internal resistance) in series with a resistor , and then connect load of two different resistances to the output port. Now the three parameters can be derived from the known values of , and the two measurements of the load voltage , corresponding to the two resistance values used.
Assume , , and the input voltage is measured to be ; also, assume the two different load resistors used are and respectively, with the two corresponding output voltage and . Find , and .