Handbook for Sound Engineers

Amplifier Design 711

under open loop conditions is much smaller than any of
the impedances used in structuring the loop. These
requirements are easily met in practice as input imped-
ances of commercial devices range upward from several
megohms while the output impedances range downward
from several tens of ohms throughout the audio
frequency range. The approximate values given for
Vo/Vi are valid if, in addition to the requirements stated
above, the magnitude of A is large throughout the
frequency range being employed. Fig. 20-11A is an
inverting voltage amplifier having an unbalanced input
as well as output. Fig. 20-11B is an inverting voltage
amplifier with a balanced input. Fig. 20-11C (unbal-
anced) and Fig. 20-11D (balanced) are examples of
more versatile configurations. The impedances Z 1 and
Z 2 can be any two terminal configurations of impedance
elements. These circuits find applications as low-pass
filters or integrators, high-pass filters or differentiators,
phase compensators, shelving filters, and tone controls
among a myriad of other possibilities. Fig. 20-11E is a
combining amplifier that combines or adds signals from
several sources with different weighting or gain factors
for each signal.
Fig. 20-12A is an example of a noninverting voltage
amplifier and Fig. 20-12B is a noninverting unity gain
voltage follower that is often employed as a buffer
because of its extremely high input impedance and
exceptionally low output impedance. In each instance
the open loop transfer function, A, is positive and real at
low frequencies.
Most of the wideband low noise operational ampli-
fiers currently available for audio applications are inter-
nally structured so as to exhibit dominant pole
characteristics. This means that the open loop transfer
function of such an amplifier exhibits the behavior of a
single-pole amplifier over the frequency range for
which it is useful. Such an amplifier is easily employed
in the majority of feedback arrangements without fear
of violating the conditions necessary for stability. Fig.
20-13 is a Bode diagram typical of such amplifiers, both
when operated open loop as well as when operated with
a closed loop noninverting voltage gain of 20 dB.
An examination of Fig. 20-13 reveals that under open
loop conditions this amplifier exhibits a gain of 90 dB or
V/V at dc with the gain being down by 3 dB
at a frequency of Hz attended by a phase
shift of 45°. The bandwidth of this amplifier is then
Hz and the product of the gain at dc with the
bandwidth or the gain bandwidth product is 10^7 HzV/V.
The loop is closed in this example by requiring that R 2 in
Fig. 20-12A be nine times the value of R 1. The second
set of curves in Fig. 20-13 describe the performance

under this closed loop condition. The curves reveal that

the gain at dc is now 20 dB or 10 V/V and that the band-

width has now become 10^6 Hz. The gain bandwidth

product is still 10^7 HzV/V. The bandwidth has been

increased by exactly the same factor that the gain was

reduced. This behavior is characteristic of dominant pole

amplifiers. The application of feedback has yielded

another important benefit. The open loop amplifier not

only had a nonflat amplitude response throughout most

of the audio spectrum, it suffered from phase or group

delay distortion above a few hertz as well. The amplifier

with feedback has a linear phase behavior from dc to

beyond 10^4 Hz and hence does not introduce any group

delay distortion in this frequency range.

20.2.4 Active Filters Employing Operational

Amplifiers

Filter technology has a long time-honored history that

actually predates electronics by several decades. In fact,

if Lord Kelvin (William Thomson) had not discovered

the physical and mathematical properties of so-called

wave filters in the middle of the 1800s, submarine tele-

graphic cable communications and later long distance

telephone communications would have been delayed

until well into the 20th century.

In spite of the voluminous literature and interest in

this subject, what will be touched on here are just a few

of the filter types that have proven to be of paramount

10 u 104

10 10

2

u

10 u 102

Figure 20-12. Noninverting voltage amplifiers.

!

!

Vi

Vi

R 1

R 2

Vo

Vo

A. Noninverting voltage amplifier.

B. Noninverting unity gain voltage amplifier.

R 1

A¾VVo

i

=

R 1 +R 2

R 1 +R 2

A +

R 1

Vo R 2

Vi

=¾1 +

Rin=¾d¾ Rout =¾ 0

"A" positive and large

at low frequencies

A¾

Vo

Vi =

1

1

(A)+ 1

Vo

Vi

=^1

Rin=¾d Rout= 0

"A" positive and large

at low frequencies