MULTISTAGE DIFFERENTIAL AMPLIFIERS

Franclim F. Ferreira, Pedro Guedes de Oliveira, Vítor G. Tavares

A method for analysing a feedback amplifier

As we have seen above, we can easily obtain the values of the gain as well as the input and output resistances, if we know the amount of feedback 1+ b A. Therefore, what we need is a method to determine in an easy way, the values of b and A.

To illustrate the procedure, we will use a series-shunt topology as an example (for the other topologies will be similar), which in its ideal form can be represented as on the picture on the right.

In a real circuit the schematic will show as in the figure depicted on the right.
Since the open loop gain should include the load effects both of the source and the load, it is necessary to incorporate the resistances Rs and RL in the basic amplifier.

Furthermore, we have to replace the feedback block by an equivalent circuit that translates the unilateral transmission from output to input and that, for the topology we are considering, should be like as shown on the right.

Using the equivalent two-port network technique, we easily obtain the desired circuit. Take notice that the choice of the independent variables is, in the output port, the sampled signal (in this case, the voltage) and, in the input port, the current, if we want a Thévenin configuration (as in our example) or the voltage, if we want a Norton configuration (adequate for a parallel comparison).

In the final circuit, the input→output transmission is ignored for the reasons above, which means to set to zero the controlled source of the output loop.

The feedback factor b is just the controlling factor of the input loop source.

Resistances Rib and Rob represent the load effect of the feedback block on the basic amplifier and therefore should be incorporated in it. We will then obtain the equivalent circuit that after some simplifying procedures will be as depicted on the right.

To evaluate A it is only necessary to set b = 0 and determine Vo / Vs.

The parameters of the feedback amplifier can be trivially obtained from the following expressions:

  • voltage gain                            Af = A / (1 + b A )

  • input resistance                       Rif = Ri (1 + b A )

  • output resistance                     Rof = Ro / (1 + b A )

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