Handbook for Sound Engineers

Amplifier Design 707

The angle of the first factor is

while the angle of the second factor is

therefore, the total phase shift is

Make a graph of I versus in order to
complete the Bode diagram. This graph also appears in
Fig. 20-7.

20.2.2 Feedback Theory

Fig. 20-8 represents a generalized feedback loop based

on a voltage amplifier. In the absence of feedback, with

the loop open, the amplifier has a transfer function A.

The feedback path has a transfer function B, the input

signal from the outside world is Vin and the signal

supplied as an output is V 0. When the loop is closed, the

input signal is combined with the feedback signal in the

indicated junction to form an error signal Ve. The

process that occurs in the junction may be either addi-

tion or subtraction, depending on the nature of A, B, and

the type of feedback (positive or negative) desired. In

any event the signal actually supplied to the amplifier

when the loop is closed is Ve.

The system contained within the dotted enclosure of

Fig. 20-8 has a rather different transfer function from

that of the amplifier operated under open loop condi-

tions. The closed loop transfer function denoted by Ac^ is

derived as follows:

(20-7)

(20-8)

(20-9)

A and B, in general, are complex functions of the

steady-state frequency of operation. The absolute

magnitude of the denominator of Eq. 20-9 is called the

gain reduction factor. The feedback is called negative

when

(20-10)

and is positive when

Figure 20-7. Bode diagram for simple ac amplifier.

A S

S

Z 0

4

+------

----------------

10 Z 0

S+Z 0

= u---------------

jZ

jZ

Z 0

4

+------

-------------------

10 Z 0

jZZ+ 0

= u-------------------

90 o

45 o

0

45 o

90 o

1.0 10

0.1 1.0 10

20 dB

0 dB

S

2

---tan

1– 4 Z

Z 0

• ©¹§·------ -

tan1– Z

Z 0

------

©¹

• §·

I S

2

---tan

1– 4 Z

Z 0

–t©¹§·------ -an1– Z

Z 0

= – ©¹§·------

log ZZe 0

Figure 20-8. Generalized feedback loop.

B

A

BV 0

Ve

Vin Vout

Ve Vin+= BV 0

V 0 =AVe

AVin+= ABV 0

Ac

V 0

Vin

=-------

A

1 – AB

----------------.=

1 –>1AB