Section I2: Feedback Amplifier Considerations

The basic structure of a generic system with feedback is shown in Figure 11.1 and is reproduced to the right. Note that this model is in the form of a signal flow diagram, with the arrows indicating the direction of signal “movement.” Note that each of the parameters shown in this illustration may represent voltage or current signals and that they may be in the form of a time function, a Laplace transform, or in complex phasor notation. For purposes of this discussion, we will be using Laplace notation as shown in the figure and focus on a negative feedback amplification system. The circle with the Σ symbol is called a summer and adds, with appropriate signs, all inputs present.

Note that, as many times before, I have slightly changed your author’s notation in an attempt to maintain consistency with previous material.

In this diagram, the specific signals may be defined as:

¾ R(s) is the source signal; ¾ ε(s) is the difference, or error, signal between the source signal and the feedback signal (defined below), or

ε(s) = R(s) − Y(s); (Equation 11.1)

Note that this is indeed a negative feedback system since the feedback signal is subtracted from the source signal.

¾ Go(s) is the or the open-loop amplifier gain; ¾ C(s) is the amplifier output and is equal to

C(s) = ε(s)Go (s) ; (Equation 11.2)

¾ H(s) is the feedback factor; and ¾ Y(s) is the feedback signal that is a function of the output signal and the feedback factor given by

Y(s) = C(s)H(s). (Equation 11.2)

Keep in mind that Go(s) and H(s) are transfer functions, which means that they represent the ratio of the output of a given block over the input to that block in Laplace transform notation. The closed-loop gain, G(s), is defined by the closed-loop transfer function, C(s)/R(s), is found by combining Equations 11.1 and 11.2:

C(s) G (s) G(s) = = o R(s) 1 + Go (s)H(s) , (Equation 11.3) where the term Go(s)H(s) is called the loop gain. The amount of feedback is defined by the denominator of Equation 11.3, or 1+Go(s)H(s) and, if the loop gain is much greater than one, the closed loop gain is approximately equal to 1/H(s). This illustrates the first of the negative feedback advantages; i.e., since the feedback network usually consists of passive components, the overall gain of the system has little dependence on the open-loop gain of the amplifier and may be made very accurate and stable (we’ve already seen this in op-amp circuits, where the amplifier response is determined by the feedback).

By combining and rearranging Equations 11.1 and 11.2 differently, we can develop an expression of the feedback signal as

G (s)H(s) Y(s) = o R(s) 1 + Go (s)H(s) .

This expression tells us that if the loop gain is very large (i.e., Go(s)H(s)>>1), the feedback signal is approximately equal to the source signal, or Y(s)≈R(s). Therefore, if a large amount of negative feedback is used, the feedback signal is almost identical to the source signal and the error signal approaches zero. This strategy is used for the input differencing circuit of an op-amp, where signals at the two input terminals are tracked, or compared.

It is implied above, but worth stating explicitly, that the source, the load, and the feedback network represented by H(s) do not load the amplifier represented by G(s) in the idealized signal flow diagram of Figure 11.1. As we’ve seen, this is not going to happen for practical systems, so we will develop a method for presenting a real circuit in terms of the ideal structure above. No big deal – we’re old hands at presenting an ideal case and then making appropriate modifications (a.k.a. “goofing with it”).

Types of Feedback

There are four basic forms of feedback as illustrated in Figures 11.2a through 11.2d (reproduced below) that are based on the signal to be amplified (voltage or current) and the desired output (voltage or current). The “Amp” of the figures may be an operational amplifier, but may also be any BJT amplifier configuration that we have studied.

In the figures below, note that there are two notations of the connections at the input and output. In the first (from your text), the output connection defines the type of feedback, the form of subtraction defines the input connection, and the order is output-input. In the second notation (in parentheses), the connections themselves are defined; i.e., shunt indicates parallel and series is just plain old series and the order is input-output.

I did not just throw this in to be cruel, the second version is a more common notation in references and, since the order is reversed, I felt that was worth any temporary (I hope) confusion.

The four forms of feedback shown above are summarized in Table 11.1, given below.

Input Output Type of Feedback Input Output Impedance Impedance Voltage feedback-voltage subtraction (series-shunt) Voltage Voltage High Low Current feedback-current subtraction (shunt-series) Current Current Low High Voltage feedback-current subtraction (shunt-shunt) Current Voltage Low Low Current feedback-voltage subtraction (series-series) Voltage Current High High