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Cascaded Op Amp Circuits Op amp circuits have the advantage that they can be cascaded without changing their input-output relationships. This is due to the fact that each (ideal) op amp circuit has infinite input resistance and zero output resistance. Although the cascade connection does not affect the op amp input-output relationships, care must be exercised in the design of an actual op amp circuit to ensure that the load due to the next stage in the cascade does not saturate the op amp. A three-stage cascaded connection. 40 Example 11 Find vo and io in the circuit. 41 Example 12 Determine vo and io . a b V 42 Instrumentation Amplifiers (a) The instrumentation amplifier with an external resistance to adjust the gain, (b) schematic diagram. 43 Instrumentation Amplifiers The IA has three major characteristics: 1. The voltage gain is adjusted by one external resistor RG. 2. The input impedance of both inputs is very high and does not vary as the gain is adjusted. 3. The output vo depends on the difference between the inputs v1 and v2, not on the voltage common to them (common-mode voltage). 44 Example 13 Let R = 10 kΩ, v1 = 2.011 V, and v2 = 2.017 V. If RG is adjusted to 500 Ω , determine: (a) the voltage gain, (b) the output voltage vo. 45 Integrator is + i f = 0 vs dvo is = , if = Cf Rs dt An op amp integrator dvo 1 =vs dt Rs C f 1 vo = Rs C f ò t to vs d +vo (to ) An integrator is an op amp circuit whose output is proportional to the integral of the input signal. 46 Differentiator An op amp differentiator An differentiator is an op amp circuit whose output is proportional to the rate of change of the input signal. The differentiating amplifier is seldom used in practical applications because it is a source of noise. Why ? 47 Cascaded Integrators Op amp 1: vg R1 + C1 dvo1 =0 dt dvo1 1 =vg dt R1C1 Op amp 2: vo1 dv + C2 o = 0 R2 dt dvo 1 vo1 =dt R2C2 d 2 vo dt 2 d 2 vo dt 2 1 dvo1 =R2C2 dt = 1 1 vg R1C1 R2C2 Cascaded integrators and differentiators can be combined in analogue computers to solve differential equations. 48 Review 1 49 Review 2 50 Review 3 For this op amp circuit, voltage vo is: 51 Review 4 For Fig. 5.40, For the this circuit op ampin circuit, current ix is: 52 Review 5 If vs = 0, current i0 is: 5.41, 53 Review 6 If vs = 8 mV, voltage v0 is: 5.41, 54 Review 7 5.41. va is: If vs = 8 mV, voltage 55 Review 8 The power absorbed in the 4-k resistor is: 56