Page 133 - Op Amps Design, Applications, and Troubleshooting

116 AMPLIFIERS

The input resistance can now be calculated, Equation (2.47), as shown;

56 fcQ(982 Q + 3 *Q)
" 982 O(l + 50,000) + 3 JbQ

= 4.54 Q.

As you might expect, the input resistance approaches the ideal value (to be driven
by a current source) of 0 ohms.
If the input frequency is higher than DC, the input resistance will deviate
more from the ideal value of 0. For example, if our input frequency were raised to
1 kilohertz, the input resistance would increase to about 226 ohms. Additionally,
we would need to consider the effects of bandwidth and slew rate limitations.

Output Resistance. The output resistance of the circuit in Figure 230 as
viewed by the load resistor is ideally infinite, as the circuit acts like a current
source. A more accurate value for the output resistance can be computed with the
following equation:

where A v is the open-loop voltage gain of the op amp at a particular frequency
and R x is the value of RI and JR 2 in parallel. In the case of Figure 2.30, let us esti-
mate the output resistance at DC:

R 0 = 50,000 x 982 O = 49,1 MQ

As evidenced in the equation, this value becomes less ideal as the frequency of
operation is increased.

2.8.3 Practical Design Techniques

A practical current amplifier circuit can be designed by applying the equations
discussed in the preceding paragraphs. Depending on the application, you will
know some combination of the following parameters:

1. Input current range
2. Output current range
3. Current gain
4. Load resistance

For purposes of a design example, let us build a current amplifier that satis-
fies the following requirements: