704 Chapter 20

may be balanced while the output is unbalanced, the
input may be unbalanced while the output is balanced,
both input and output may be balanced, or both input
and output may be unbalanced. The balanced configura-
tion is preferable when dealing with long lines and low
signal levels or where ground isolation is required. This
preference is based on the common mode rejection
properties of the balanced arrangement. For example,
consider the signal leads in Fig. 20-3 to be a long
twisted pair contained within an electrostatic shield with
the shield grounded. The electrostatic shield offers no
noise immunity from external time-varying magnetic
fields. When such varying magnetic fields exist, a noise
signal will be induced between each of the signal
conductors and ground. The amplifier, however, ampli-
fies the difference that appears between its input termi-
nals and hence any common signal between the input
terminals, and ground is rejected.

20.2.1 Amplifier Transfer Function

The relationship that exists in the steady state between
the output signal and the input signal of a two-port
device such as an amplifier or filter is called the transfer
function. The transfer function has a magnitude and an
angle with each being dependent on the steady state
signal frequency. Mathematically, the transfer function
is expressed concisely in the form of a complex func-
tion that has both real and imaginary parts. The magni-
tude of the transfer function at any particular frequency
is the square root of the sum of the squares of the real
and imaginary parts and physically corresponds to the
ratio of the output signal amplitude to the input signal

amplitude. The angle of the transfer function at any

particular frequency is the angle whose tangent is the

ratio of the imaginary and real parts and physically

corresponds to the phase difference between the output

signal and the input signal. These ideas are best

expressed by a simple example. Consider a dc-coupled

voltage amplifier that offers an amplification of 10 volts

per volt (V/V) at dc or zero frequency and an amplifica-

tion of 10/ V/V at a frequency f 0 while having intro-

duced a phase shift of S/4 radian, or 45°. Upon

denoting the transfer function by the symbol A and the

independent frequency variable by the symbol f, the

following statements can be made:

(20-1)

or more compactly

(20-2)

where,

G is the magnitude of the transfer function or gain func-

tion,

H is the base of the natural logarithm,

I is the angle of the transfer function or phase function,

the angle whose tangent is the imaginary part divided

by the real part of Eq. 20-1,

G is the square root of the sum of the squares of the real

and imaginary parts of Eq. 20-1,

j is.

(20-3)

Figure 20-2. A typical reinforcement and reproduction chain.

Microphone

Phonograph

Tape

Front

loudspeaker

Delayed

loudspeaker

Auxiliary

DVD

CD^1 / 3 octave

equalizer

(^1) / 3 octave
equalizer
Signal
delay
Power
amplifier
Power
amplifier
RIAA
equalizer
Mixer
Figure 20-3. An amplifier as a two port device.
Signal Input Amplifier Output Load
2
A
10
1 f
f 0
©¹§·----^
2

• 
  

  ---

  
  

  j
  10–
  f
  f 0

  
  

  ---

  
  

  1
  f
  f 0

  
  

  ©¹
  +§·^2
  = + -----------------------
  AGH
  jI

  
  

  1–
  G^10
  1
  f
  f 0
  ©¹§·--- -^
  2

  
  


• 
  

  = ---------------------------