DIFFERENTIAL AMPLIFIER, DIFF-AMP

An amplifier that produces an output signal proportional to the difference of the two input signals. It has a very large gain when opposite signals are applied to the inputs as compared to the negligible gain resulting from common inputs. Commonly used for the input stages of an operational amplifier.

BASIC CIRCUIT The circuit has two separate inputs, two outputs,

and both emitter terminals are connected together.

MODES OF SIGNAL OPERATION:SINGLE-ENDED INPUT

Case 1: Vi1 ≠ 0 and Vi2 = 0 Input signal is applied to B1 ( Vi1 ≠ 0 ). B2 is grounded ( Vi2 = 0). Inverted amplified output signal, Vo1, appears at terminal

C1. A signal voltage Ve appears in phase at the emitter of Q1

and Q2 which becomes an input to Q2. Q2 functions as a common-base amplifier. Noninverted amplified output signal, Vo2, appears at

terminal C2. Voltage gain Av1 = - Rc / re. Voltage gain Av2 = +Rc / re.

CONFIGURATION

Case 2: Vi2 ≠ 0 and Vi1 = 0 Input signal is applied to B2 ( Vi2 ≠ 0 ). B1 is grounded ( Vi1 = 0). Inverted amplified output signal, Vo2, appears at terminal

C2. A signal voltage Ve appears in phase at the emitter of Q1

and Q2 which becomes an input to Q1. Q1 functions as a common-base amplifier. Noninverted amplified output signal, Vo1, appears at

terminal C1. Voltage gain Av2 = - Rc / re. Voltage gain Av1 = +Rc / re.

CONFIGURATION

DIFFERENTIAL INPUT Two opposite-polarity input signals are

applied to the inputs ( double-ended operation).

Vi1 and Vo2 are in phase. Vi2 and Vo1 are in phase. There is a 180° out-of-phase relationship

between Vo1 and Vo2. / Vo1/ = / Vo2/

COMMON-MODE INPUT The same input is applied to both input

terminals. The output signals for both transistors are

equal to zero

COMMON-MODE REJECTION RATIO, CMRR The ratio between differential voltage gain and

common-mode gain. The measure of an amplifier’s ability to reject

common-mode signals. CMRR = ∞ (ideal).

CMRR = Avd / Acm

Where: Avd = differential voltage gain Acm = common-mode gain

Expressed in decibels CMRR = 20 log ( Avd / Acm)

OPERATIONAL AMPLIFIER An op-amp is a high gain differential amplifier with

high input impedance (Zi) and low output impedance (Zo). An op-amp contains several stages of differential amplifier to achieve a very high voltage gain.

Typical op-amp unit

The concept of negative feedback is used in several op-amp applications. Negative feedback is the process whereby a portion of the output voltage of an amplifier is returned to the input with a phase angle that opposes the input signal.

OUTPUT VOLTAGE Op-amp provides an output component that is due to

the amplification of the difference of the signals (Vd) applied to the two inputs and a component due to the signals common to both inputs(Vc).

Vo = AdVd + AcVc

Where : Vd = difference voltage Vd = Vi1 – Vi2

Vc = common voltage ( unwanted)

Vi1 + Vi2

Vc = -------------- 2

Ad = differential gain Ac = common mode gain

Ad >> Ac

COMMON MODE REJECTION RATIO, CMRR

The measure of an amplifier’s ability to reject unwanted signals. The main purpose of differential connection is to amplify the difference signal while rejecting the common signal (noise) at the inputs.

CMRR = Ad Ac CMRRdB= 20 log Ad Ac

Vc

Vo = AdVd 1 + ------------- CMRR Vd

CMRR = infinite (ideal) the larger the value, the better the circuit operation Vo = AdVd + AcVc

Vo = AdVd 1 + AcVc AdVd

DC OFFSSET PARAMETER (output error voltage)

Unwanted voltage and current generated by the internal circuitry and not by the applied input signal.

INPUT OFFSET VOLTAGE; VIO (1mV ~ 6mV) When Vi = 0, the circuit acts like an

noninverting amplifier.

Vo(offset) = VIO [ 1 + Rf / R1 ]

INPUT OFFSET CURRENT;IIO (20nA ~ 200 nA) An offset current due to the difference in

currents at the two inputs.

Vo(offset) = IIO Rf 

TOTAL OUTPUT OFFSET VOLTAGE

Vo(offset) = VIO [ 1 + Rf / R1 ] + IIO Rf 

INPUT BIAS CURRENT , I IB

I+IB + I-

IB

IIB = --------------- 2I+

IB = IIB + IIO

2I-

IB = IIB - IIO

2IIO = I+

IB - I-IB

FREQUENCY PARAMETERS

fc = f1 / AVD

Where B1 = unity- gain BW f1 = unity- gain freq AVD = voltage differential gain = open loop voltage gain = 200V/mV typical = 20V/mV (min)

CUTOFF FREQUENCY, fc

SLEW RATE, SR Slew rate is the maximum permissible rate at which op-amp

output can change in volts per microsecond. If the rate of output voltage change is greater than SR, the output signal will be distorted.

SR = ΔVo / Δt

Vo = ACL Vi

ΔVo / Δt = ACL [ ΔVi / Δt ] SR = ACL [ ΔVi / Δt ]

MAXIMUM SIGNAL FREQUENCY The input frequency of an op-amp is dependent on both the

bandwidth and slew rate parameters

ws < SR/ K

K =output gain factor K = ACL Vi

SAMPLE APPLICATIONS

INVERTING AMPLIFIER

Vo = - (Rf / R1) Vi

Zi = R1 + Rf / AOL ≈ R1

Zo = [ AOL / ( 1 + AOL)] Rf // Zout

Zo ≈Zout

Where Zout = open-loop output impedance Zin = open-loop input impedance AOL = open-loop gain Zi = input impedance of the inverting amplifier Zo = output impedance of the inverting amplifier

B = feedback fraction AOL(mid) = midrange open-loop gain fi = signal frequency fc = critical frequency BWCL = closed-loop BW

NONINVERTING AMPLIFIER

Vo = [ 1 + Rf / R1 ] Vi

Zi = [ 1 + AOLB ] Zin

Zo = Zout / ( 1 + AOLB)

UNITY FOLLOWER A voltage buffer configuration provides a means of

isolating an input signal from a load.

Vo = ViB = 1

ACL = 1Zi = ( 1 + AOL) Zin

Zo = Zout / ( 1+ AOL)

SUMMING AMPLIFIER

Rf Rf Rf Vo = - ------ V1 + -------- V2 + ---------V3

R1 R2 R3

INTEGRATOR

DIFFERENTIATOR

VOLTAGE DIFFERENCE

INSTRUMENTATION AMPLIFIER

Vo = [1 + 2Rf / RG ] ( V1 – V2 )

Let R1 = R3 = R2 = R4 = R

Rf1 = Rf2 = Rf

PHASE-SHIFT OSCILLATOR Oscillator is a circuit that produces periodic (repeating)

waveforms on its output with only the dc supply as a required input.

fo = 1_____ 2Π√6 RC

B = 1 / 29

ACTIVE FILTERS

First-order LPF Fourth-order LPF

Values for Butterworth Response

Order Roll off ratedB/Decade

First stagePoles

First stageDF

Second stagePoles

Second stageDF

Third stagePoles

Third stageDF

1 20 1 Optional

2 40 2 1.414

3 60 2 1.0 1 1.0

4 80 2 1.848 2 0.765

5 100 2 1.0 2 1.618 1 0.618

6 120 2 1.932 2 1.414 2 0.518

FUNCTION GENERATOR

12

X1k

X10k

R7

C8

X10

C1

12

12

0

X100

Vz2

R8

2

1

1 2

R1021

X1

1 2

R1

12

0

R2

R6

R11

2

1

C13

12

X10

C7

C12

12

C10

X1k

12

R4

X1

C 5

C140

0

Vz1

12

1 2

X100

C11

C4

C9

C2

X1

1 2

12

X1k

1

3

2

411

OUT

+

-

V+V-

C15 X10k

0

C3

X10k

R9 21

X100

12

1 2

12

1

3

2

411

OUT

+

-

V+V-

R5 21

X1012

C6

Vout

12

1

3

2

411

OUT

+

-

V+V-

R3