The circuits looked at so far depended for their functioning on linear feedback. The magnitude of the signal returned to the negative input was always strictly proportional to that of the output voltage. The result was that within the limits set by the op-amp, the magnitude of the output voltage is proportional to that of the input signal. Often we want to create a more complicated response. For example,
· the output signal should not exceed a particular value, regardless what happens on the input.
· The output voltage should be proportional to the log of the input voltage.
During this lab you will examine two circuits, one in which non-linear feedback is used to achieve a particular response or transfer function, the other uses non-linear feedback to stabilize the amplitude of an oscillator.
1. The full wave rectifier.
The full wave rectifier is a circuit that tries to realize the transfer function Vout = |Vin|. The circuit is shown in figure 1.
It is most convenient to analyze its function by considering separately what happens for Vin > 0 and Vin < 0. Figure 2a shows the equivalent circuit for Vin > 0. In this case the diode D1 is reversed biased and effectively an open circuit, D2 is conducting. The feedback loop is effectively a single resistor, from the output of OA2 to the negative input of OA1. OA1 and OA2 act together as a single op-amp and the complete circuit acts like a simple voltage follower, Vout = Vin. There is a complication with this circuit. At sufficiently high frequency, both OA1 and OA2 introduce 90º phase shifts, which together with the 180º shift achieved by feeding the signal back to the input of OA1, would make the circuit unstable. A small capacitor, C, is used to counteract this.
The equivalent circuit for Vin < 0 is shown in figure 2b. The circuit around OA1, just the diode D1 which is biases in the forward direction, acts as a voltage follower. D2 is now reverse biased an effectively an open circuit. As a result, the + input of OA2 is grounded and OA2 is configured as inverter. Thus we have for Vin < 0, Vout = ‑Vin.
The equivalent circuit for Vin < 0
Assemble the circuit, initially with C = 100 pF, and check that it works as advertised for various wave forms (f = 1 kHz). Increase the frequency until you can clearly observe the problems that arise when the circuit switches over from Vin < 0 to Vin > 0 mode. What is the typical switching time? Can you improve this by changing C? Observe that without C the circuit becomes unstable when Vin > 0.
NOTE: DECOUPLE SUPPLY LINES CLOSE TO THE OP-AMP WITH 0.1mF capacitors
NOTE: The circuit requires two op-amps. You can get two op-amps in a single package, which saves in power supply connections and makes it possible to build a compact circuit. Use the dual op-amp AD712 in this circuit.
2. The Wien bridge oscillator
The Wien bridge oscillator can be understood most readily by first considering the transfer function of the RC network that forms the feedback loop. Calculating V2/V1 we find
For wRC = 1 the signal at the input of the amplifier is exactly in phase with that at the output, and if the amplifier has a gain of at least 3 (to compensate for the factor 1/3 in V2/V1) the circuit will oscillate with a frequency f = 1/2pRC. When the gain of the amplifier is slightly larger than 3, the output amplitude will grow until it saturates the amplifier, when the gain is less than 3 it will decay until the oscillator stops. The problem is how to make an amplifier that has a gain of exactly 3.
The principle of the Wien bridge oscillator.
A possible solution is shown in Fig. 4. A gain of +3 amplifier is made using an op-amp with the usual feedback circuit (R1, R2). The feedback is made slightly amplitude depend by connecting a non-linear network between points x, x parallel to R1. The simplest network is a pair of diodes. When the output amplitude is large, the diodes conduct better, their resistance is smaller and the gain of the circuit drops. Similarly, a small output voltage results in more gain.
Assemble the circuit shown in Fig. 4, initially without the diodes. Adjust R1 until the gain is close to 3 and the circuit starts to oscillate. Add the diodes, and again adjust R1 to obtain a stable oscillation. You should do this first in EWB, following exactly the same steps as if you were building the circuit in hardware. Note that it takes time for the oscillations to build up to their final amplitude, and that this is quite dependent on the value of R1. Also, keep in mind that if there were absolutely no noise, the circuit would not start to oscillate, since this requires an initial disturbance. The "ideal" elements in EWB have no noise associated with them. Therefore, it is important to make sure that for the op-amp you implement the "real" device, here the OPA27 from the Burr-Brown collection. Since the gain of the amplifier is dependent on the output voltage, the sine wave is slightly distorted. The easiest way to bring out the distortion is to differentiate the output of the oscillator a few times. To do this, build two differentiators using a dual op-amp (AD712), as shown in figure 5.
Figure 5. Two differentiators in series to look at sine wave distortion.
The distortion can be reduced considerably with a circuit element in the feedback loop which has a response time that is much longer than the oscillator period. A simple solution is to use a small light bulb. The resistance of the filament is a function of its temperature, which again is determined by the power dissipated in it. To see how this works, modify your circuit along the lines indicated in fig. 6. The output amplitude can be adjusted with R1. Explain why the control elements (previously the diodes, now the lamp) have changed position in the feedback loop. Observe that the distortion is strongly reduced. Try to determine approximately the response time of the light bulb.