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Effects of operational amplifier (op-amp) non-idealities.

Consider each effect in turn creating output error voltages Vo due to each non-ideality inturn, with the op-amp otherwise considered ideal.

Imagine other voltage inputs (for non-inverting v+ or inverting v ) short circuited (s/c) to0V, then find total output effects by superposition.

Note that the dc power supply rails, Vs are not shown in the following diagrams.

1. Offset voltage, Vos = v v+Vos may be positive (+ve) or negative (ve).

(a) Non-inverting amplifier: input signal, vin heading towards non-inverting (+) input

v

_

+

vin

=0V

vo=Vo

due to Vos

R1

0V

15k

Rf60k

Vos

I

v+

non-inverting amplifier circuit diagram

1

os

R

VI , and the same current also flows through Rf,

so the voltage drop across Rf is IRf = f1

os RR

V

This gives an error output voltage, Vo = Vos + IRf = Vos + f1

os RR

V= os

1

f VR

R1

For this circuit the offset error voltage, Vos is multiplied by the same numerical voltage gain

as for normal vin input signals, ideal non-inverting gain, Av =1

f

R

R1

normal output, vo = Avvin

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(b) Inverting amplifier: input signal or level, vin heading towards inverting () input

60k Rf

15k Rin_

+vin

0V vo

0V

Vos

I

I

inverting amplifier circuit diagram

As for the previous circuit,in

os

R

VI , and the same current also flows through Rf,

so again the voltage drop across Rf is IRf = fin

os RR

V

This gives an error output voltage, Vo = Vos + IRf = Vos + fin

os RR

V= os

in

f VR

R1

Thus both inverting and non-inverting have error due to Vos, Vo= osf VR

R1

with appropriate R.

However, for this inverting circuit the gain for Vos is not the sameas the gain for normalinput vin signals.

Normal inverting numerical voltage gain, Av =

in

f

in

o

R

R

v

v assuming ideal op-amps

Signal output, vo = Avvin

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2. Bias current effects

Data sheets give average bias currents, IB+ and IB, (or i+ and i ), flowing into (or out of)

the non-inverting (+) and inverting () inputs as IBIAS =2

IIBB

.

The input offset current error source is Ios = IB+IB = i+ i

Ideal op-amp operation brings v+ to the same voltage as v.

v+ = i+RB v= i+RB giving I =1

B

1R

Ri

R

v

, IF = I i=1

B

R

Ri i

Vo = v+ + IF RF = i+RB + F1

B

RiR

Ri

=

F

1

F1B

RiR

RRRi

Then make RB = F1F1

RR

RR

, which is the parallel combination of R1 and RF,

giving error Vo = FOSFFF RIR.iiRiRi

This allows the remaining error due to Ios to be nulled or trimmed out by similar methodsas used for Vos

A similar analysis for the non-inverting amplifier shows that the inclusion of RB as belowcan help reduce bias current errors for this circuit too. (parallel combination shorthand R1 RF)

error Vodue to bias

currents

+RB

RF

i

v

i

R1

0V

v+

V1=0V

error Vodue to bias

currents

+

R1

RF

i+

v

i

RB

I

0V

v+

V1=0V

IFinverting amplifier

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3. Estimate effects due to errors, specified limits & practical component tolerances.Check which are dominant - which do need dealing with - for good performance over therequired dynamic ranges.Make good use of manufacturer's datasheets and application hints.

(a) Check the likely effects of the resistor tolerances, of resistor pairs not being perfectly

matched and of op-amp non-idealities. Estimate potential variations from ideal theory dueto realistic component tolerances. Resistor values may be 5%, capacitor values may be

20%, for instance. Variations due to tolerances and due to time or temperature drifts maybe reduced by using expensive precision components, if required by the application.

(b) Before practically testing an amplifier circuit, try nulling the op-amp's offset to minimise

Vos and Ios errors (with the 15V supply rails connected), eg for the A741by connecting

the v+ and v inputs to 0V and adjusting vo to 0V using a variable resistor between pins 1

and 5 with its wiper connected to 15V, or by using the summing input. Alternatively, anop-amp with a better specification (spec) may be needed.

(c) Add appropriate resistances (RB) to minimiseIBIAS effects.

(d) To predict the frequency response of a linear op-amp circuit from dc upwards:

The frequency, fH, where the output voltage has reduced from its steady mid-band/low f

value by2

1, corresponds to the 3dB half-power point.

Operational amplifiers without external components limiting their low frequency gainnormally provide no lower frequency limit, they will amplify down to dc, so fL = 0 Hertz,

and bandwidth (BW) = fH fL = fH

For regions where the numerical gain multiplied by the bandwidth (BW) is constant(gain.BW product = constant = unity gain BW), the bandwidth can be estimated by usingthe unity gain BW from the op-amp specifications (eg the manufacturer's datasheet).

The BW at some other gain is ideally a scaled version of this, found by dividing by the new

non-inverting numerical gain, so new fH = new BW =gainnew

productBW.gain

(e) To practically estimate slew rate = maximum rate of change of vo, try square wave

inputs with increasing frequency to a unity gain buffer amp, measure maxt

Vo

in V/s.

For sinusoidal input & output signals and an output amplitude Vp, (where Vp = Av input

amplitude): slew rate = sV/in10Vf2dt

dv 6pmax

max

o

When Vp is at its maximum, then fmax is the full power bandwidth.

(f) Check limits (clipping distortion) due to dc power supply rail voltages, Vs.