When d-c signals are to be amplified, the usual approach is to use a direct-coupled circuit. The difficulty

of maintaining sufficiently low drift in a direct-coupled configuration led to the development of chopper and chopper-stabilized circuits, where a mechanical chopper

reduces drift to low values. Unfortunately, other shortcomings arise, and in most applications the

direct-coupled d-c amplifier would be preferable if the drift could be reduced to an acceptable value. The

advantages over the chopper or the chopper-stabilized types include rapid recovery from overload, freedom from hash, simplicity and small size due to absence of transformers

and capacitors

Middlebrook, R. D.

Taylor, A. D.

Caltech Authors - Main

Differential Amplifier 
With Regulator Achieves 
HIGH STABILITY, LOW DRIFT 
Unique circuit configuration of this direct-coupled difje1·ential amplifier makes pos-
sible low drift and high common-mode 'rejection ratio. Meets requirements of mis-
sile telemet'ry systems 
WREN d-e signals are to be ampli-
fied, the usual approach is to use a 
direct-coupled circuit. The diffi-
culty of maintaining sufficiently 
low drift in a direct-coupled con-
figu ration led to the development 
of chopper and chopper-stabilized 
circuits, where a mechanical chop-
per reduces drift to low values. Un-
fortunately, other shortcomings 
arise, and in most applications the 
direct-coupled d-e amplifier ·would 
be preferable if the drift could be 
+E, 
-£, 
By R. D. MIDDLEBROOK, 
California Insti tute of Technology, 
A. D. TAYLOR, 
Microdot, lnc., So. Pasadena, Cal. 
reduced to an acceptable value. The 
advantages over the chopper or the 
chopper-stabilized types include 
rapid recovery from overload, free-
dom from hash, simplicity and 
small size due to absence of trans-
formers and capacitors. 
A d-e amplifier for airborne or 
missile telemetry use must meet 
many specifications. The usual re-
quirements for differential input, 
single-ended output, signal levels 
and linearity are easy to meet. 
FIG. 1-Basic circuit of the amplifier. Voltages E , and E , a1·e obtained 
from a reference diode string fed /?·om the power supply. Resistor R . serves 
as a gain con trol 
56 
Those which are difficult to achieve, 
especially simultaneously, are low 
drift over a wide temperature 
range, stable though adjustable 
gain, wide frequency response, 
high input impedance, high com-
mon-mode rejection factor, insensi-
tivity of performance to source re-
sistance, small size, weight and low 
power requirements. The d-e am-
plifiers described here provide ex-
ceptional performance in all these 
respects simultaneously. There is 
no unique set of specifications, 
since the design can be tailored 
for particular applications. 
The following figures are typical: 
gain stability ± 0.75 percent; fre-
quency response ±1 percent to 10 
Kc, 3 db down at 50 Kc; differential 
input resistance greater than 1 
megohm; common-mode rejection 
factor 120 db to 400 cps, 100 db to 
2 Kc, for common-mode voltage ±5 
v peak and for a gain of 1,000. The 
gain is adjustable over a 2-to-1 
range with maximum preset to any 
value between 200 and 1,000. For 
a gain of 1,000 the maximum dif-
ferential input signal is ±5 mv 
peak. The output capability is ±5 
v into 20,000 ohms with output re-
electronics 
The low-drift tmnsistor d-e am]Jlific>· tmde>· test. To alleviate tempemture 1Jroblems, differential antplifie1• uses a 
1wir of matched transistors in one can 
sistance less than 100 ohms, and 
with up to 100 percent offset ad-
justment. The drift is to some ex-
tent a function of the signal source 
and a typical equivalent input drift 
is ± 100 p.v for eight hours over a 
temperature range of 25 C to 100 C. 
For extreme temperature en-
,·ironments, an amplifier is avail-
able with an internal heater so that 
eight-hour input drifts of ±100 p.v 
can be maintained over ambient 
temperatures from -55 C to 100 
C. Size and weight are tailored to 
meet environments, and are typic-
ally 3 cubic inches and 4 ounces for 
the heaterless models. Required 
power supplies are 20 rna at plus 
and minus not less than 18 v ± 1 
percent. The model containing a 
heater is about 7.5 cubic inches, 
weighs 6 ounces, and requires arr 
additional input of up to 300 rna 
(for -55 C ambient) at +28 v 
unregulated. 
The circuit of the heaterless d-e 
amplifier is shown in Fir. 1. Tran-
sistors Q, .. and Q,IJ form a differen-
tial first stage, Q •• and Q,s a differ-
ential second stage. and Q. and Q, 
form the single-ended t h ird and 
July 28 , 1961 
fourth stages. Overall negative 
feedback is taken from load resist-
ance R. and applied in series with 
the differential input. Resistance R. 
is an internal load; any external 
load is connected between output 
and ground. The circuit is inher-
ently capable of converting a differ-
ential input to a single-ended out-
put, and is superior in three 
respects to a circuit which is differ-
ential throughout and in which only 
one output of the two is used: the 
output resistance is considerably 
lower for the same loop gain, much 
better common-mode rejection is 
obtained, and fewer transistors are 
required. 
With zero input signal, there is 
no voltage between the output ter-
minal and ground. Internal load 
resistance R, is connected to nega-
tive supply voltage E1 to permit 
operating current to flow in out-
put stage Q, under qu iescent condi-
tions. 
With a differential input signal, 
input 1, for example, goes positive 
and input 2 goes an equal amount 
negative. The cut·rent in Qu in-
creases while that of Q,a decreases. 
The current changes in resistances 
R. (both) cause the input voltage 
to Qu to decrease and that of Q.B 
to increase. The increased current 
in Q.a causes an increased voltage 
drop across R ,, and reduces the in-
put voltage to emitter-follower 
stage Q.. The lower emitter volt-
age of Q, causes an increase in t he 
base-emitter voltage of Q., hence Q, 
conducts more current through R, 
and the output voltage goes up. A 
resistance from the emitter of Q. 
to negative supply voltage -Eh to 
provide correct operating current, 
is not shown in the schematic. A 
fraction of the voltage between out-
put and ground is injected in series 
with the input through negative 
feedback path R,., Ru, RIB and R.B. 
Transistor Q, does not act as a 
constant-current sink for the cur-
rents in Ru and RLB, as it would 
if resistance R. were returned to a 
fixed supply voltage. Instead, t he 
connection allows Q, to fulfill two 
important requirements. Imagine 
that the half of the circuit contain-
ing Q,a and Q.B is folded over to lie 
on top of t he half containing Q,, 
and Qu (see F ig. 2). The path 
57 
X 
+ 
E, 
FIG. 2-Differential stages folded 
over and drawn to 1·eveal a voltage 
1·egulator circuit 
from point X through Q,, Q,,., s and 
Q .... s back to point X is a voltage 
regulator circuit in which (E, -
E,) is the reference, and (Ez + 
E,) is t he regulated output voltage. 
Transistor Q, is the error ampli-
fier, and Q. is the series element 
whose current is controlled by Q,'. 
Transistor Q, does not contribute 
to this mode of operation of the 
circuit, and serves merely to trans-
mit the collector current variations 
of Q. to the base of Q,. 
The voltage between X and the 
negative suply -E, is constrained 
to be closely equal to (E, - E,) 
(R. + R,) 1 R;. The higher the com-
mon-mode loop gain, designated Ge, 
the more highly regulated will be 
the voltage E z at X. Since the volt-
age across each R. is approximately 
E, - Ez, the collector currents of 
Q,. and Q,s are stabilized, which is 
the first of the two functions of Q •. 
Each collector current is set to 100 
p.a, this low value being chosen to 
make the noise contributions of 
Q,. and Qu small, and to allow a 
large value of R. which makes the 
common-mode loop gain Gc large. 
To understand the second func-
tion of Q,, it must be recognized 
that in the presence of arbitrary 
voltages at the two amplifier inputs, 
the collector current of Q. contains 
both differential and common-mode 
components. These result from 
conditions imposed by the feedback 
path. A high value of Ge permits 
the collector current of Q. to adjust 
as required to the inputs, while 
the collector currents of Qu and 
Q,_., and hence their base currents, 
hardly change. Thus, the second 
function of Q. is to maintain high 
58 
signal impedances at the inputs to 
Q,. and QLB. 
There is typically about_ 45 db of 
overall negative feedback in the 
complete amplifier, which implies a 
differential loop gain of about 200. 
This high value ensures low output 
resistance, high differential input 
resistance, and stable gain deter-
mined essentially by the feedback 
elements. Close, but not necessarily 
exact, equality between R,_. and R,s, 
and between R ..,. and R u , is re-
quired. Under these conditions, 
gain G, from input 1 and gain G, 
from input 2 may be written G, 
(Ru + R.,.)jR ,,. 
G, = G, [ 1 + _R~ (~1!2_ - tJ.R, ) J R, R. R, 
where R ,. = RlB = R, Ru = R .s 
= R ., R ,s - R ,. = t:J.R, and R .s -
R.,. = !!.R,. For a gain of 100, typi-
cal values are R, =1 K and R. = 
100 K, hence for small percentage 
unbalances t:J.R,;R, and tJ.R,; R , the 
gain G. is very nearly the same as 
G,. Both gains are determined by 
R u and R._,, with only weak de-
pendence on R,8 and R u . The fre-
quency response of the amplifier 
can be controlled by capacitance 
CA, with only weak dependence on 
Cs. 
The degree of rejection of com-
mon-mode input signals is sensitive 
to asymmetry in the resistance 
pairs R, and R,. The amplifier com-
mon-mode rejection factor C, de-
fined as the ratio of the common-
mode input voltage to the differen-
tial input voltage which produces 
the same output voltage, is given 
by 
_l_ = [~ (I-_!_)- tJ.R, ]/a C R. Ge R. 
where G, = G, = G, and Ge is the 
common-mode loop gain previously 
defined. The value of C is maxi-
mized by adjustment of R OB and Cs, 
which may be designated as com-
mon-mode adjustments with neg-
ligible effect on the gain or on the 
frequency response. However, the 
converse is not true. Any attempt 
to alter the gain by changing R.,. 
would have a disastrous effect on 
the common-mode rejection factor. 
Means must be found to change the 
effective ratio of R u to R.,. without 
destroying the symmetry. 
Gain variation can be accom-
plished by bridging a gain control 
resistance between symmetrical 
tapping points on R.,. and R u , as 
shown in Fig. 3A. In the gain equa-
tions, R.,. (or R!B) should then be 
replaced by the effective value R., 
given by R,E = R. + 2 (R, + R.) 
(R, - R . ) ! R .. 
It is possible to achieve gains 
variable over a two-to-one range 
without interaction between the 
gain and common-mode adjust-
ments. 
Care must also be taken to avoid 
upsetting the optimum common-
mode rejection when changing the 
quiescent output level. The most 
convenient way to introduce an out-
put level control which satisfies this 
requirement is to remove R .s from 
its ground connection and to return 
it to the slider of a potentiometer 
across the supply voltages. The im-
pedance level of the potentiometer 
must be low enough that the effec-
tive value of R u is changed by an 
acceptably s m a 11 percentage 
throughout the desired level range, 
to avoid undue degradation of the 
common-mode rejection factor. 
Alternatively, the common-mode 
adjustment can be reset for a par-
ticular output voltage level. 
In the presence of a level control, 
the lower output terminal remains 
at ground, as shown in Fig. 3B. 
The amplifier common-mode re-
jection factor is sensitive to un-
balance in the signal source re-
sistances. If the rejection factor is 
adjusted to be infinite with equal 
source resistances, the common-
mode rejection factor C' in the 
presence of an unbalance tJ.R. in the 
source resistances is given by 1/ C' 
= tJ.R,jfJ,R,Gc where f3, is the com-
mon-emitter current gain of Q,.. or 
QLB. It is the absolute and not the 
percentage unbalance of the source 
resistances which is significant. A 
typical value for C' is 10", or 120 
db, for t:J.R, = 100 ohms, therefore 
_the common-mode rejection factor 
is little affected by normal source 
resistance unbalances. 
Although the above description 
of the amplifier indicates excellent 
characteristics with respect to its 
signal-handling capabilities, the 
crucial test of a d-e amplifier is its 
drift performance. Drift in a di-
rect-coupled d-e amplifier origi-
electronics 
nates almost exclusively in the dif-
ferential input transistors, and 
arises primarily because of aging 
and temperature changes in the 
saturation currents, the base-emit-
ter voltages, and the current gains. 
Use of silicon transistors with 
room temperature saturation cur-
rents in the order of 1 na (milli-
microamp) effectively eliminates 
this source of drift with normal 
]ow-impedance signal sources such 
as st rain gages and thermocouples. 
However, the other two drift 
sources are important. 
The base-emitter voltage of a 
silicon transistor is stable with 
time but exhibits marked tempera-
ture dependence, decreasing by ap-
proximately 2 mv for every degree 
centigrade rise in temperature. 
Even though the base-emitter volt-
age drops of Qu and Q,. are in 
series opposition, and even if Qu 
and Q,. are exactly matched, an 
equivalent input drift of 20 p.v will 
result for every 0.01 deg C tempera-
ture differential between these two 
transistors. The availability of two 
matched transistors in one can, the 
FSP-2 of Fairchild Semiconductor 
Corp., has alleviated the problem of 
temperature differentials. 
In addition to this effect, there is 
also a drift source due to unavoid-
able unbalance in the temperature 
dependences of the base-emitter 
voltages in Qu and QlB. In the 
double unit, the values of dV •• jdT 
are typically matched to about 1 
par t in 100, but even this would 
give rise to an equivalent input 
drift of 20 p.V for every degree 
change in ambient temperature. 
This is unacceptable, but because 
Ra 
R,. }· OUT 
the base-emitter voltage at constant 
current is closely linear with tem-
perature, compensation is possible. 
The conrpensation function is pro-
vided by an auxiliary circuit which 
supplies a current linearly depend-
ent on temperature!, As shown in 
Fig. 1, this current is injected at 
a tapping point on the resistance 
Ru or R,., thus generating a volt-
age in series with the inputs which 
is linearly dependent on tempera-
ture. Adjustment of the tapping 
point permits the inherent un-
balance of dV •• jdT in Qu and Q,. 
to be reduced by a factor of as 
much as 100. The equivalent input 
drift from this cause can be held 
to about 20 p.v over a range of 100 
deg C. This high degree of cancel-
lation depends upon closely equal 
temperatures of Qu , Q,. and the 
compensating circuit, an equality 
which is in turn limited by the 
thermal design. 
The remaining source of drift is 
the variability in the current gains 
of Qu and Q,.. Since the collector 
current of each transistor is stabil-
ized by Q,, each base current flows 
through the resistance of its signal 
source and thereby gives rise to a 
spurious input signal. It is appar-
ent, that the drift performance of 
the amplifier cannot be specified 
independently of the signal-source 
characteristics. However, perform-
ance can be so specified that the ex-
pected drift can be determined for 
a particular source configuration. 
A typical value for the current gain 
of a double unit is 40 at 25 C, with a 
possible unbalance between the two 
units of about 10 percent. Since in 
the amplifier each collector current 
Ru 
R,. 
+E, 
OUT! 
(B) 
FIG. 3-ln troduction of a gain con trol by bridging resistance across sym-
met?·ical tapping points on R ..., and R,B, in (A); introdu ction of a level 
control by connecting R ,B to a low-impedan ce pot entiomete1· across a bias 
voltage, (B) 
July 28, 1961 
is stabilized at 100 p.a, each base 
current is nominally 2.5 p.a at 25 C. 
If the ambient temperature in-
creases, each base current decreases 
fairly linearly at about 15 najdeg 
C, again with a possible unbalance 
between the two units of about 10 
percent. These figures make pos-
sible an estimate of the tempera-
ture drift in the presence of given 
source resistances. For example, 
if the source resistance in series 
with each input is 0.5 K, then an 
equivalent input drift up to ±0.1 
(0.5 X 15) = ± 0.75 p.v per deg C 
could be expected. The fact that this 
drift is approximately linear with 
temperature permits compensation. 
If the source resistance is known, 
drift due to current gain changes 
can be cancelled along with that 
due to base-emitter voltage changes 
a nd it is necessary to set the tem-
perature compensation adjustment 
in the presence of the desired 
source resistances. There then re-
mains only drift due to the varying 
base current flowing in any un-
balanced source resistance. For ex-
ample, if the 500 ohm SOI,Irce re-
sistances were unbalanced by 5 
ohms, an uncompensated equivalent 
input drift of about 0.075 11v per 
deg C would result. 
The examples indicate the de-
pendence of the amplifier drift per-
formance on the signal-source con-
figuration. If the drift thus obtain-
able is undesirably great, or if in-
dependence of the source configura-
tion is desired, it is necessary to 
use an internal heater to eliminate 
temperature-dependent changes in 
the amplifier parameters. The 
heater used in these amplifier 
models is continuously controlled 
by an internal subsidiary amplifier 
referenced to a thermistor sensor, 
and the main amplifier temperature 
is maintained very nearly constant. 
As a result, low drifts can be 
achieved over wide ambient tem-
perature ranges. 
The assistance of C. E. Everest is 
gratefully acknowledged. 
REFERENCES 
( 1) R. D. Middlebrook : D es ign of Tra n-
sistor Regulated P ower Supplies , P roc 
IRE, 45, p 1,502, ~ov 1957. 
(2 ) W. T. Matzen a n d J . R. Bia rd, Dif-
feren tial Amplifier F eatures d-e S tability , 
E LECTRONICS, J a n. 16, 195 9. 
59 


Differential amplifier with regulator achieves high stability, low drift

http://authors.library.caltech.edu/36427/1/Middlebrook_1961p56.pdf

Differential amplifier with regulator achieves high stability, low drift

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main