# Designing a Poor Man s Square Wave Signal Generator. EE-100 Lab: Designing a Poor Man s Square Wave Signal Generator - Theory

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1 EE-100 Lab: - Theory 1. Objective The purpose of this laboratory is to introduce nonlinear circuit measurement and analysis. Your measurements will focus mainly on limiters and clamping amplifiers. During these experiments you will learn about the following important concepts: virtual ground property, and nonlinear saturation. Also you will learn how to design a clipping circuit, and design a poor man s square wave signal generator. 2. Introduction: limiters, clamping amplifiers, clipping circuits The purpose of the amplitude limiter is to modify signals only if their amplitude exceeds a certain level. Beyond this amplitude the signal is abruptly clipped. We will present design considerations on the feedback circuit which performs limiting by clipping all waveforms above a given magnitude. Amplitude limiters are often required in many systems where the amplitude of a signal cannot be allowed to exceed some prescribed positive or negative limits. This function is often achieved by utilizing resistor/zener diode networks. A typical Zener diode has the following characteristic: + v - i i forward current, i f Zener voltage, -V z leakage current 0 V f v reverse current, i z Figure 1 Zener diode characteristic The forward characteristic of a Zener diode is the same as a typical diode characteristic. Note that as the reverse voltage is increased the leakage current remains essentially constant until the breakdown voltage is reached where the current increases dramatically. This breakdown voltage is v = -v z called the Zener voltage. The forward voltage is called the Zener diode ON voltage (v f ). While for the conventional diode it is imperative to operate below its breakdown voltage; the Zener diode is 1

2 intended to operate at that voltage, and has applications mainly as a voltage regulator. Notice that Zener diode has a constant (negative) voltage v z across a wide range of currents making it an ideal voltage reference. It should be noted that Zener diode limiters are useful mainly for protection against overvoltage and not as a means of obtaining precisely known limits for signal processing or computation purposes. Nevertheless, a Zener diode in the feedback network of an op-amp will accomplish a limiting function by clipping the input waveforms and by limiting to a given region. The following figure shows a Zener diode feedback limiter. Figure 2 Zener diode feedback limiter: a) circuit, b) transfer characteristic The circuit works as a classical inverting amplifier except that the voltage amplitude is limited to the Zener diode voltages. The maximum amplitude level cannot exceed the sum of the Zener diode OFF voltage (v z ) and the Zener diode ON voltage (v f ). We can set the slope of the linear region (with properly chosen R 2 and R 1 values) and the saturation level (changing the Zener diode) as well. Virtual ground property - Since the non-inverting input terminal of the op-amp is grounded, the opamp tries to keep the inverting input (S) at ground as well through a negative feedback accomplished by the R 2 resistor. Assuming an ideal op-amp model, in the limit case (input currents of op-amp input terminals are zero, and the voltage between them are zero as well) the inverting input terminal is also grounded. Then S is called a virtual ground, a node that will stay at ground as long as the circuit is working, even though it is not directly connected to ground. Remark: The ideal op-amp model is also called virtual short circuit model because for purposes of analysis it is equivalent to connecting a short circuit across the op-amp input terminals, and demanding that the current through it is zero at all times. It is not just an efficient tool for simplifying analysis but it has also practical relevance because this property makes possible e.g. resistance measurement without cutting any wires of a circuit. 2

3 Figure 3 shows a limiter based on a resistive ratio method. Figure 3 Diode bridge limiter: a) circuit, b) transfer characteristic The difference from the previous circuit is that this circuit contains passive elements only and the transfer characteristic is non-inverting. The input voltage is copied to the output linearly (the slope is always 1) until it exceeds the voltage level determined by the voltage dividers see the corresponding transfer characteristic. To understand how this circuit works we drew three different cases in Figure 4, i.e. a) circuit working in the linear region, b) in the positive saturation, and c) in the negative saturation. Figure 4 Diode bridge limiter, a) linear region, b) positive saturation, c) negative saturation 3

4 Notice that currents flowing through R 1 and R 2 have directions always as shown in Figure 4. Diodes do not enable reverse current direction. Let us suppose we are in the linear region. Using KVL (along D 1 and D 2 ) we get the output voltage as v out = v in + v D1 v D2 = v in. We assumed that diodes have the same threshold voltages. We would get the same result if we wrote KVL along D 3 and D 4. Now let us examine the saturation regions. Suppose we are in the linear region and we are continuously increasing the input voltage toward high positive values. The current i 1 flowing through R 1 will be smaller and smaller because the voltage through R 1 will be smaller. At the same time the current i L through R L will be larger because the output voltage is increasing as well. But i L cannot be larger than i 1 because it has positive additive term only from the +V C power supply through resistor R 1 and diode D2 (i 1 > i D2 > i L write KCLs to check this statement). The limit case is when i 1 equals to i L. This belongs to the positive saturation as shown in Figure 4.b. In this case, R 1 and R L form a voltage divider saturation level was derived assuming ideal diodes. D 1 and D 4 are closed because they have negative reverse voltage. They can be considered as open circuits. We get very similar results for negative saturation as well. 4

5 EE-100 Lab: Experiment Guide Exp 1: Build an inverting amplifier (Figure 2). You will be provided a box specially designed for this measurement (Figure 5: Limiter - 1). Do not connect any Zener diode yet. Use V DD =12V and V SS = - 12V. Refer to the basic lab experiment on how the power supply should be connected!) Let R 1 and R 2 be 1k and 4.3k, respectively. Remember if you need to modify a circuit, it is safer for the circuit if you disconnect first the input signal and turn the DC power supply output off. Checking the virtual ground property Set the input signal V in to a constant value in the range of [-5V; +5V]. Determine at least 10 measurement points. (Use the 6V DC power supply output for V in.) 1-a) Set different constant input voltage and measure with your DMM at each step the voltage level at the inverting input terminal of the op-amp. Watch both input and output on the scope. Explain the condition under which the virtual ground property is valid. 1-b) Now, open the feedback loop (do not connect R2 to the inverting input terminal of the op-amp). Repeat the previous measurement. What is the difference? Summarize the necessary conditions for valid virtual ground property. Clipping measurements Build the circuit shown in Figure 2 connect Zener diodes. 1-c) DC measurement: Measure the transfer characteristic of the circuit. Draw the chart of the output versus input voltage in the range of [-5V; +5V]; What is the level of the saturation? 1-d) AC measurement: Set the input signal to 1 khz, 500mV V PP, 0.0 VDC offset sine wave from the function generator. Observe the input and output waveforms using the first and second channel of your scope. Is there any clipping? Now, set the scope to display the transfer characteristic (X/Y mode). What does the transfer characteristic look like? Explain. 1-e) AC measurement: Now, set the input signal to higher Vpp continuously using voltage level control of the function generator (up to ~ 1-2 Vpp). Observe and draw the input and output for the case that gives clipping. Determine the saturation level and draw the transfer characteristic. Hint: to determine the saturation level more exactly you might change to X/Y mode or select a more appropriate waveform. Poor Man s Function Generator 1-f) Set the maximum Vpp output at the function generator. Observe and draw the input and output waveforms. Is this output waveform good for a square wave generation? 1-g) Let s make a better square wave generator. Disconnect the R2 resistor from the feedback loop (from the inverting input terminal of the op-amp). Observe and draw the input waveforms. What are the requirements for the input signal to produce a square wave output signal (hint: change the amplitude of the input signal)? 1-h) Let s build the simplest and cheapest square wave generator. Remove also the Zener diodes from the feedback loop. Repeat the previous measurement. Now, what are the requirements for the input signal to produce a square wave output signal? This circuit works as a null level comparator and this is the simplest one to produce square wave (assuming a periodic input signal). 1

6 Exp 2: Build the diode bridge limiter shown in Figure 3. Use the box Figure 5: Limiter - 2. Set R 1, R 2 to 10k, and R L to 1k. Set +V C and V C to +12V and 12V, respectively. 2-a) Set the input signal to a 1 khz, 1.0 V PP, 0.0 VDC offset sine wave from the function generator. Observe the input and output waveforms using the first and second channel of your scope. Now, set the scope to display transfer characteristic (X/Y mode). How does the transfer characteristic look like? Explain. 2-b) Now, set the input signal to a 1 khz, 5.0 V PP, 0.0 VDC offset sine wave from the function generator. Display the transfer characteristic (X/Y mode). Draw the transfer characteristic. Compare this transfer characteristic to the op-amp Zener feedback circuit. What are the differences? What are the reasons for that? 2-c) Replace the R 2 to 4.3k. Set the input signal to a 1 khz, 5.0 V PP, 0.0 VDC offset sine wave from the function generator. Display and draw the transfer characteristic (X/Y mode). How does the transfer characteristic look like? What are the differences in comparison with the previous measurement? Explain it. 2

7 Appendix: You will use special boxes designed for this laboratory measurement (Figure 5). V+ = +12V V- = -12V V+ = +12V V- = -12V V + D 1 D 2 1N749A, 4.3V R 1 10kΩ R 2 D 1 D 2 V in R 1 1kΩ - 4.3kΩ AD823AN + V out V in 1N4148 R L V out D 3 D 4 Limiter - 1 R 2 10kΩ, 4.3kΩ V- Limiter - 2 Figure 5 Boxes designed for this laboratory measurement. a) Limiter 1: Zener diode feedback limiter, b) Limiter 2: Diode bridge limiter The arrangement of the components of each box matches the corresponding schematic. Boxes require power supply refer to the basic lab guide what the proper connection is. You can see labels showing which banana socket belongs to the positive power supply (V+= +12V, and red color), the common terminal (always in the middle), and the negative power supply (V- = -12V). Do not mix them. If you fill unsure ask your TA to help you. Passive components (resistors, capacitors, etc) are prepared in advance you need only to put them to the proper small banana sockets. Large banana sockets on the left side of the box are used for input, while sockets on the right for the output. If you need to set DC input voltage you can use the 6V output of the power supply. To set periodic input voltage using the function generator you can use BNC-banana converters. Also, there are prepared banana plugs with small pins so you can connect the alligator clips of the scope probe and measure any desired signal. 3

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