Tutorial 4

ASIA PACIFIC UNIVERSITY OF TECHNOLOGY & INNOVATION

Analogue Electronics Tutorial Questions Tutorial 4 – The Operational Amplifier .

The op-amp circuit shown in Figure  is excited by a sinusoidal voltage source  cos t. Find the output voltage vo(t). (Hint: Convert the circuit to its frequency-domain representation.)

Figure 

1

.

The circuit in Figure  shows an op-amp configured as an ideal integrator. The capacitor C accumulates the charge flowing through R, thereby giving rise to an integral effect on the input voltage. a)

Show that the given operational amplifier circuit is an integrator, i.e., vo(t) ∝ ∫ vs(t) dt.

b)

Why won’t the circuit work as a practical integrator as given? How might this problem be overcome? (Hint: Consider what would happen if a small  component was present in the input voltage.)

Figure 2

2

.

The circuit in Figure  is a model of an op-amp stage in which the offset voltage and current are shown. a)

Determine the signal component Vo in terms of the difference signal V1 – V2, assuming that the op-amp is ideal (IB1, IB2, Iio and Vio are zero).

b)

Determine the component of Vo caused by

c)

Determine the component of Vo caused by Vio only.

d)

For V1 = V2 = , find the worse-case offset voltage at the output. Given that Vio =  mV; Iio = . µA; IB = . µA; R1 =  kΩ; R2 =  kΩ.

I io only. 2

R2

V1

R1 IB1

V2

R1

R2

_Vio +

_ Vo

Iio 2 + IB2

Figure 3

3

.

Consider the op-amp in Figure , where we assume Vio =  and Ro = . (Note that the diagram on the right shows the internals of the op-amp shown in the diagram on the left.) a)

Show that the output voltage Vo2 due to IB2 only is − R′RRi Av Vo 2 = I (Ri + R1 )(R′ + R ) + RR′ − Av RRi B2

b)

Show that the output voltage Vo1 due to IB1 only is R1Ri (R′ + R )Av Vo 2 = I (Ri + R1 )(R′ + R ) + RR′ − Av RRi B1

c)

Show that if IB2 ≅ IB1, then Vo1 + Vo2 is minimised by taking R1 =

Figure 

4

RR ′ . R + R′

.

An instrumentation amplifier is often used to amplify the output from a transducer bridge as shown in Figure . For example, in a strain gauge, the resistance R1 are precision fixed resistors. The resistance R2 + ∆R is the transducer attached to the structural member under test. Because of the load on the structure, the resistance changes. The resistance R2 in the remaining arm of the bridge is a dummy gauge (unloaded) and is used to balance out resistance variations caused by variations in temperature and other parameters. a)

Assuming that the gain of the instrumentation amplifier is AD, show that for

δ=

∆R