EE 323 – Op-amp 1

_____ OP-AMPS _____

I. PRACTICAL OP-AMP

• High gain differential amplifier, A. • High input impedance, zin . • Low output impedance, zout. • Applications: voltage amplitude changes (amplitude and polarity), oscillators,

filter circuits, and many types of instrumentation circuits.

Noninverting input

Inverting input

Output

+VCC

-VEE

A.vin

zout Zin

vin

+

_

vout A + _

vin

Symbol Schematic

EE 323 – Op-amp 2

• two power supplies: +VCC and –VEE, (some op-amps can operates using a single supply).

• input, vin, difference between two input voltages: non-inverting & inverting . • single-ended output. • very high input impedance, zin, (MΩΩΩΩ) • very low output impedance, zout, (less than 100ΩΩΩΩ) • very high voltage gain, A. • output voltage:

vo=Avin

CLASS B PUSH-PULL AMPLIFIER

GAIN STAGE

DIFF. AMPLIFIER

vin vout

OP-AMP

EE 323 – Op-amp 3

1. Op-Amp input characteristics

1. Input bias current

• ββββDC of each transistor is slightly different • Base currents in the differential amplifier

are slightly different. • Input bias current is defined as the

average of the DC base currents:

2II

I 2B1B)base(in

++++====

• Typical in nanoamperes (BJT) or picoampares (FET)

• Flows through the resistances between the bases and ground.

• Resistances may be discrete resistances or may be Thevenin resistances of the input sources.

Different base current

EE 323 – Op-amp 4

2. Input offset current

• Defined as the difference of the DC base currents: Iin(off) = IB1 – IB2 • Indicates how closely the transistors are matched. • Data sheet of an op-amp lists Iin(base) and Iin(off), • Base currents can cause output voltage error in precision applications. • Compensate resistor may be use to eliminate this effect.

a) Base resistor produces unwanted input voltage b) Equal base on other side reduces error voltage

EE 323 – Op-amp 5

3. Input offset voltage

More errors caused by mismatch of the differential amplifier stage: - collector resistances (RC1≠≠≠≠ RC2) and - base-emitter voltages (VBE1≠≠≠≠VBE2) .

Input offset voltage is defined as the input voltage that would produce the same output error voltage in a perfect differential amplifier.

EE 323 – Op-amp 6

AV

V error)off(in ====

Output of diff. amp includes desired signal and error voltage

Total error: Vin = v1 – v2

Vout = A(v1 – v2)

EE 323 – Op-amp 7

DC error inputs: V1err = (RB1 - RB2)Iin(bias)

V2err= (RB1 + RB2)Iin(off)/2 V3err = Vin(off) Verr = A (V1err + V2err + V3err)

Table 1: Sources of Output Error Voltage

Description Cause Remedies

Input bias current Voltage across a single RB Use equal RB on other side

Input offset current Unequal current gains Data sheet nulling methods

Input offset voltage Unequal RC and VBE Data sheet nulling methods

EE 323 – Op-amp 8

2. The 741 op-amp

EE 323 – Op-amp 9

a. Final stage The quiescent output is ideally 0V Any deviation from 0V is the output error voltage. Output swing is within 1 to 2V (due to drops inside the op-amp).

b. Frequency compensation

Capacitor CC is a compensating capacitor. Miller effect causes this capacitor become a large input capacitance:

Cin = (A+1)CC A=gain of Q5 and Q6.

CC generates a cutoff frequency of 10Hz The op-amp has an ideal Bode plot.

AOL

100dB

10Hz 1MHz freq.

EE 323 – Op-amp 10

c. Bias and offsets (741C op-amp compensation and null) • RB neutralizes the effect of input bias current (80nA). • 10K potentiometer is used to null or zero the output voltage (no input

signal). • Eliminates the effect of 20nA input offset current and 2mV input offset

voltage.

EE 323 – Op-amp 11

d. CMRR

• 90dB at low frequency • Degrades at higher frequency (curve (a)).

EE 323 – Op-amp 12

e. Maximum peak-to-peak output Depends on the load resistance connected to its output (curve (b)).

f. Short circuit current Max short circuit current 25mA = Max current produced by 741.

g. Frequency response • Unity frequency of 1MHz (curve (c)). • Worthless for higher frequency applications. (Other high frequency op-

amps are available).

h. Slew rate • Compensation capacitor, CC, prevents oscillations (negative feedback)

would interfere with the desired signal. • Also creates a speed limit on how fast the output can change.

• This relates to the slew rate, defined as:

where SR is the slew rate and equals to the change in output voltage divided by the change in time.

tvS out

R ====

EE 323 – Op-amp 13

• Slew rate represents the fastest response that 741 can have (0.5V/µµµµs) (i.e., the output of a 741C can change no faster than 0.5V in a microsecond (figure (c)).

• Slew rate also affects the response

of sinusoidal signal.

• Slew rate limits the large-signal response (specifies in the data sheet.)

EE 323 – Op-amp 14

• The initial slope of a large sinusoidal signal, can be derived as: SS = 2ππππfVp

• To avoid slew-rate distortion, SS has to be less than or equal to SR • The max frequency at which the signal is on the verge of slew-rate distortion is:

p

Rmax

pSR

V2S

f

fV2SS

====

========

fmax= power bandwidth or large-signal bandwidth of the op-amp. Two bandwidths to be considered when analyzing the op-amp operation:

- The small-signal bandwidth determined by the first order response of the op-amp (by compensation capacitor)

- The large-signal or power bandwidth determined by the slew rate. Examples: 18-1 to 18-4 (page 628).

EE 323 – Op-amp 15

II. IDEAL OP-AMP

Ideal op-amps are used to simplify the op-amp circuit analyzing.

. Gain A≡≡≡≡∞∞∞∞ . zin=∞∞∞∞

. zout=0 . input currents I+=0

. input current I_=0 . va=v+ - v-=0

vo=Ava ⇔⇔⇔⇔ va=vo/A=vo/∞∞∞∞

Operation depends on external connection

Output

+VCC

-VEE

Avin

zout=0 zin=∞∞∞∞

va=0

I+=0

I_=0

EE 323 – Op-amp 16

1. INVERTING AMPLIFIER:

• Inverting amplifier uses negative feedback to stabilize the overall voltage gain of the amplifier.

• Gain of the op-amp is too high and unstable to be used without some forms of feedback.

I+=I_=0, va=0 (ideal op-amp):

CL

unity)CL(2

)CL(in

)CL(

ino

in1Ro

inin1R

inina

A

ff

2Rz2R1RA:Gain

2R1Rvv

2R1Rv1Riv

2Rv

ii0_II

2Rv

i0v

====

====

−−−−====

−−−−====

−−−−====−−−−====

================

========

++++

RL

R1

vo vin

R2

iin _ +

iR2

~ va

EE 323 – Op-amp 17

• Open loop configuration: 1. Open loop gain, A(OL), 2. Open loop cutoff frequency f2(OL).

• Feedback configuration: 1. Close loop gain, A(CL), 2. Close loop frequency f2(CL). 3. Gain = 0dB (i.e., gain=1=unity) f(unity).

Example: 18-7

Gain A(dB)

A(OL)

A(CL)

f2(CL) f2(OL) funity frequency

EE 323 – Op-amp 18

2. NON-INVERTING AMPLIFIER:

Feedback amplifier provides an output voltage in phase with the input voltage.

Example: 18.10

1R2R1A:Gain

)2R1R1(vv

1R2R

vv1Rivv

ii0I2R

vi

)CL(

ino

inin2Rino

2R1R

in2R

++++====∴∴∴∴

++++====

++++====++++====

========

====

−−−−

R1

vo vin

R2

+ _

iR2

~ va=0

EE 323 – Op-amp 19

3. SUMMING AMPLIFIER:

(multiple voltage sources: using superposition)

Example: 18-12 Problem: 18-22, 18-26 Try: 18-9, 18-11,18-13,18-21,18-23,18-27

R3

vo v2

R2 _ + ~

)2v2R3R

1v1R3R

(vo +−=

v1

R1

~

EE 323 – Op-amp 20

4.THE INTEGRATOR

Output is proportional to the integral over time of the input signal (example, a constant input vi yields a ramp output).

−−−−==== dtvRC

1v io

5.THE DIFFERENTIATOR

Output is proportional to the differential over time of the input signal (example, a ramp input vi yields a constant output).

dtdv

RCv io −−−−====

vi

R _ +

~ vo

C

vi

R

_ +

~ vo

C

EE 323 – Op-amp 21

6. THE INSTRUMENTATION AMPLIFIER

Very High Input Impedance

ca

dabRR

R)RR2(A

++++====

------ DO ASSIGNMENT #1 (posted in the class website) -----

+ _

+ _

_ +

vb

va

Ra Rb

Rc Rd

Rc Rd

Rb

vo