2. Describe and analyze the operation of several types of comparator circuits. Describe and analyze the operation of several types of summing amplifiers. Describe and analyze the operation of integrators and differentiators.

4.  The comparator is an op-amp circuit that compares two input voltages and produces an output indicating the relationship between them.  The inputs can be two signals (such as two sine waves) or a signal and a fixed dc reference voltage.  Comparators are most commonly used in digital applications. Digital circuits respond to rectangular or square waves, rather than sine waves. These waveforms are made up of alternating (high and low) dc levels and the transitions between them.

5.  The inverting (-) input is grounded to produce a zero level and the input signal voltage is applied to the noninverting (+) input as shown in Figure 1.  The incoming signal drives the amplifier into saturation producing a square-wave output. Figure 1: Op-amp as a zero-level detector

6.  When the sine wave is positive, the output is at its maximum positive level.  When the sine wave crosses 0, the amplifier is driven to its opposite state and the output goes to its maximum negative level.  Can be used as a squaring circuit to produce a square wave from a sine wave. Figure 2: Op-amp as a zero-level detector

7.  Connecting a fixed reference voltage source to the inverting (-) input.  Using a voltage divider to set the reference voltage, V REF :  Where +V is the positive op-amp dc supply voltage Figure 3: Nonzero-level detectors

8.  As long as V in is less than V REF, the output remains at the maximum negative level.  When the input voltage exceeds the reference voltage, the output goes to its maximum positive voltage. Figure 4: Nonzero-level waveform

9. The input signal in Figure 5(a) is applied to the comparator in Figure 5(b). Draw the output showing its proper relationship to the input signal. Assume the maximum output levels of the comparator are ±14V. Figure 5

10. -Noise (unwanted voltage fluctuations appears on the input line) - Noise can cause a comparator to erratically switch output states

11.  Effects of noise on a zero-crossing detector  One way to reduce the effect of noise is by using a comparator with positive feedback  This circuit is usually called a Schmitt trigger  The positive feedback produces two separate trip points that prevent a noisy input from producing false transitions (i.e. UTP and LTP) – Hysteresis  UTP – upper trigger point  LTP – lower trigger point How to reduce noise effect

12. R1R1 R2R2 V in V out +V -V Figure 6: Comparator with positive feedback for hysteresis

14. Determine the upper and lower trigger points for the comparator circuit in Figure 7. Assume that +V out(max ) = +5V and -V out(max) = -5V. Figure 7 Answer: V UTP = +2.5V, V LTP = -2.5V

15.  The output swing of a zero-crossing detector may be too large in some applications.  In some applications, necessary to limit the output voltage levels of comparator to a value less than provided by the saturated op-amp.  We can bound the output by using a zener diode – limit the output voltage to the zener voltage in one direction

16. Dz R +V -V V in V out -0.7V +V z 0  The anode of the zener is connected to the inverting input.  When output voltage reaches positive value equal to the zener voltage – limit at that value  At negative output, zener acts as a regular diode and becomes forward biased at 0.7V – limiting the negative output voltage.

17. Dz R +V+V -V V in V ou t +0.7V -V z 0  The cathode of the zener is connected to the inverting input.  The output voltage limits in the opposite direction.

18. Dz 1 R +V+V -V V in V ou t Dz2 V z2 + 0.7V - (V z1 + 0.7V) 0 Two zener diodes arranged – limit the output voltage to the zener voltage plus forward biased 0.7V (positively and negatively).

19. Determine the output voltage waveform for Figure 8. Figure 8

20. Over Temperature Sensing Circuit Analog-to-Digital (A/D) Conversion

22.  Summing amplifier has two or more inputs.  Its output voltage is proportional to the negative sum of its input voltages. V OUT = - (V IN1 + V IN2 + V IN3 + … + V INn ) Figure 9: Summing amplifier with n inputs

23.  When R f is larger than the input resistors, the amplifier has a gain of R f /R.  A summing amplifier can be made to produce the average of the input voltages.  n = number of inputs R f /R = 1/n

24.  Is a summing adder with each input having different gain  The R f to input resistance ratio would determine what the voltage output would be with a signal present at each output.

25. Determine the output voltage for the summing amplifier in Figure 10 (a) and (b). Figure 10 (a)Figure 10 (b)

27.  The feedback element is a capacitor that forms an RC circuit with the input resistor.

28. When a constant positive step input voltage is applied, the output ramp decreases negatively until the op-amp saturates at its maximum negative level. The integrator can be used to change a square wave input into a triangular wave output. The rate of change of the output voltage:

29. (a) Determine the rate of change of the output voltage in response to the input square wave, as shown for ideal integrator in Figure above. The output voltage is initially zero. The pulse width is 100us. (b) Describe the output and draw the waveform.

30.  Use a resistor in parallel with the capacitor in the feedback path.  The feedback resistor R f, should be large compared to the input resistor, R in, in order to have a negligible effect on the output waveform.

32.  The capacitor is the input element, and the resistor is the feedback element.  A differentiator produces an output that is proportional to the rate of change of the input voltage.

33. When input is a positive-going ramp, the output is negative (capacitor is charging) When input is a negative-going ramp, the output is positive (capacitor is discharging) – current is the opposite direction

34. Determine the output voltage of the ideal op-amp differentiator in Figure above for the triangular-wave input shown.

35.  Adding R in, in series with the capacitor to act as a low-pass filter and reduce the gain at high frequencies.  The resistor should be small compared to the feedback resistor in order to have a negligible effect on the desired signal.