Download Section I2: Feedback Amplifier Considerations

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)G o (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:
G(s) =
G o (s)
C (s)
=
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
Y (s) =
G o (s)H(s)
R(s)
1 + G o (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.
Type of Feedback
Voltage feedback-voltage
subtraction (series-shunt)
Current feedback-current
subtraction (shunt-series)
Voltage feedback-current
subtraction (shunt-shunt)
Current feedback-voltage
subtraction (series-series)
Input
Input
Output
Output Impedance Impedance
Voltage Voltage
High
Low
Current Current
Low
High
Current Voltage
Low
Low
Voltage Current
High
High