Prelab 11

Note: 741 op-amps are more forgiving and work better for this experiment

This lab demonstrates two novel uses of op-amps: negative impedance converters (NICs) and general impedance converters (GICs). To understand how these circuits work, you need to analyze them in sinusoidal steady-state operation or using frequency-domain methods.

1. Negative-Impedance Converters

• The NIC shown in figure 1 uses a 356 op-amp and resistors to produce an input impedance of Z_in = -Z.  Design and build a NIC with Z_in = -10kΩ. Choose the resistors R to keep the op-amp supply current from exceeding its maximum for the rated range of input voltages. Also keep in mind that the op-amp circuit only acts as a NIC so long as it is not operating in saturation.  

• Put a voltage source and two 10kΩ resistors in series with your -10kΩ NIC and take measurements to verify that the NIC really behaves as -10kΩ. You'll want to take voltage measurements at points in the circuit other than the op-amp inputs to minimize ringing that can be caused by connection of a probe.

2. General Impedance Converters

• Figure 2 shows a GIC which is built using two op-amps and five impedances. The input impedance of a GIC is given by Z₁ Z₃ Z₅/(Z₂ Z₄).

• Build a GIC to simulate (act as) a 10kΩ resistor using two 356 op-amps and five resistors.
• Use this simulated resistor in series with a real 10kΩ resistor to build a voltage divider as shown in figure 3. Drive the voltage divider with a 1kHz, 1V peak-to-peak sine wave. Does the output look like what you would expect?

• A typical use of GICs is to simulate inductors. If Z₂ or Z₄ is a capacitor and the other impedances are resistors, then Z_in is the impedance of an inductor. GICs are used to simulate inductors because it is virtually impossible to build an inductor as part of an integrated circuit, whereas op-amps, capacitors and resistors are relatively easy to build. Modify your GIC such that it acts like a 10H inductor.
• Use your "ideal'' 10H inductor in the RL circuit shown in figure 4. Determine the circuit's time constant τ. (One method of finding τ is to use an input square wave of period 10τ to represent a step input and measure the 10% to 90% rise time from which τ can be computed as in lab 3.)
• Show that this is the time constant you would expect if the inductor and resistor were both ideal.
• Increase the amplitude of the input voltage until the output becomes distorted. Why does the response of the circuit with the simulated inductor depart from the ideal response?