Network Analysis Laboratory
EEE 117L Network Analysis Laboratory Lab 3
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EEE 117L Network Analysis Laboratory Lab 3 – Introduction to Opamps and Diodes
Lab Overview
The objective of Lab 3 is to introduce students to some basic applications of operational amplifiers and diodes, and also how to measure the performance of these circuits using both Spice simulations and the Digilent Analog Discovery 2 on the circuits constructed.
Prelab
Before coming to lab, students need to complete the following items for each of the opamp circuits studied in this lab : • Any hand calculations needed to determine the values of components used in the
circuits such as resistors and capacitors, or specifications such as gain and bandwidth. • A Spice simulation of each opamp circuit to get familiar with how it functions, and
determine what to expect when the circuit is built and its performance is measured.
Connecting DC power to the Opamp
All operational amplifiers require DC power to operate, so the first step in building any opamp circuit is to connect the DC power supplies. Breadboards have rows of pins at both the top and bottom intended for use as the power supplies, which are typically labeled + and – and also color coded red for the positive power supply and blue for the negative power supply. On most breadboards these rows are connected all the way across (on some breadboards there is a break in the middle of the row). This means that DC power can be connected anywhere in the row, although it is good practice to connect the power supplies as close as possible to the circuit which will be using the power. This helps to minimize the effects of the parasitic resistance, inductance, and capacitance of the breadboard connections on the supply voltages used by the circuit. Bypass capacitors are usually added between each power supply and ground to reduce noise on the supply. An example of an opamp with the DC power supplies connected is shown in Figure 0.
Figure 0.
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Circuits to be studied
Use ± 5V power supplies for all of the opamp circuits in this lab. When choosing resistors use standard values available to you and keep all values between 1 kW and 100 kW. Use a 1 Vpp sine wave at 1 kHz as the input signal for all tests unless otherwise noted. 1. Unity Gain Buffer
One of the simplest amplifiers that can be built using opamps is the unity gain buffer shown in Figure 1.a, which has a voltage gain of 1. It is a special case of the non-inverting amplifier shown in 2 below, with R2 = 0 (a short circuit) and R1 = ¥ (an open circuit). It is often used to shield a sensitive analog circuit from a load that, if connected directly to the circuit, would cause errors. For example in the circuit shown in Figure 1.b R1 and R2 act as a voltage divider to attenuate the input signal by a specific amount (e.g., 1/5). If a load resistor were connected directly to the Vp node this would change the fraction of Vin seen at Vp. But if this same load resistor is connected to the output of the opamp, Vout, then the extremely low output resistance of the opamp allows it to drive the load without any significant change in Vp. Tip: If you need to verify that an opamp is working correctly, an easy way to do this is to connect the opamp as a unity gain buffer and check to see that it gives a gain of 1. Design the circuit in Figure 1.b to attenuate the input signal by 1/5 ± 10%. Before constructing the circuit use Spice to verify that the voltage gains from Vin to Vp , from Vp to Vout , and from Vin to Vout are all as expected. Then construct the circuit and measure these same voltage gains. Add a 10 kW load resistor to the Vout node to see how this changes the voltage gain. Then add this same load resistor to the Vp node to see how this changes the gain. Interview question: If the resistors used to construct the circuit in Figure 1.b have a tolerance of ± 5% , then how much variation will there be in the nominal attenuation factor of 1/3 when millions of these are manufactured?
Figure 1.a
Figure 1.b
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2. Non-inverting Amplifier To achieve a positive voltage gain greater than 1 the non-inverting amplifier in Figure 2. can be used. For this opamp circuit the voltage gain is given by :
𝐴" = 𝑉&'( 𝑉)*
= 1 + 𝑅. 𝑅/
Key concept: Opamp circuits use negative feedback around a voltage amplifier (the opamp) which has a very high open-loop voltage gain (typically > 100dB) to trade this high open-loop gain for high accuracy in the closed-loop voltage gain. Design the circuit in Figure 2. to achieve a voltage gain of 5 ± 10%. Before constructing the circuit use Spice to verify the voltage gain from Vin to Vout is as expected. Then construct the circuit and measure this same voltage gain. 3. Inverting Amplifier To achieve a negative voltage gain the inverting amplifier in Figure 3. can be used. For this opamp circuit the voltage gain is given by :
𝐴" = 𝑉&'( 𝑉)*
= − 𝑅. 𝑅/
Design the circuit in Figure 3. to achieve a voltage gain of -4 ± 10%. Before constructing the circuit use Spice to verify the voltage gain from Vin to Vout is as expected. Then construct the circuit and measure this same voltage gain. 4. Summing Amplifier A variation of an inverting amplifier which allows multiple input voltages to be summed together with different gains is the summing amplifier shown in Figure 4. It has the transfer function :
𝑉&'( = −1 𝑅2 𝑅/ 𝑉/ +
𝑅2 𝑅. 𝑉.3
Figure 2.
Figure 3.
Figure 4.
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More input voltages can be summed together by adding more input resistors in parallel with R1 , R2 and applying each new input voltage to its own resistor. (i.e., apply V3 to R3) Key concept: The virtual ground at the negative opamp terminal allows the gains for each input to be set independently, so one can be changed without affecting the others. Design the circuit in Figure 4. to have voltage gains of -2 for V1 and -4 for V2 , both ± 10%. Before constructing the circuit use Spice to verify the voltage gain from each input to Vout is as expected. Then construct the circuit and measure these gains. 5. Voltage limiting circuits using diode clamps It is often useful to limit the maximum or minimum output voltage of a circuit (or both), for example as a simple way to convert a sine wave into a square wave. A semiconductor device called a diode can be used for this, since the voltage across a diode stays nearly constant as the current through it varies. A diode can be thought of as a one way valve, that only allows current to flow in one direction while blocking it in the opposite direction. The symbol for a diode is shown in Figure 5.a. If a positive voltage VD of ~ +0.7V is applied across the diode, then a current ID will flow through the diode in the positive direction as shown. This is referred to as “forward biasing the diode”. But if VD is negative, then the current through the diode ID is ~ 0. This is referred to as “reverse biasing the diode”. Tip: The forward bias voltage across a diode is typically assumed to be +0.7V for hand calculations, but can actually vary between ~ +0.5V and +0.8V depending on the size of both the diode and ID. (Larger currents or smaller diodes result in higher values of VD , while smaller currents or larger diodes result in lower values of VD .) Also the reverse bias current flowing through a diode is typically assumed to be 0 because it is so small, but it is actually a few picoamps (10 -12 A) up to a few nanoamps (10 -9 A), depending on the size of the diode. (Larger diodes have larger reverse bias leakage currents). An example of a circuit that limits the output voltage in both the positive and negative direction using diode clamps is shown in Figure 5.b. In this circuit if Vo tries to go above V1 then it is limited to a maximum of ~ V1 + 0.7V when D1 turns on. And if Vo tries to go below V2 then it is limited to a minimum of ~ -(V2 + 0.7)V when D2 turns on. For (V1 + 0.7)V > Vo > -(V2 + 0.7)V both D1 and D2 are turned off, and so don’t affect the output voltage Vo.
Figure 5.a
Figure 5.b
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Design the circuit in Figure 5.b to limit the maximum/minimum output voltage Set the maximum output voltage to be Vo(max) = +2.7V, and the minimum output voltage to be Vo(min) = -0.7V. Also set the voltage gain to be ¾ between these limits. All specifications have a tolerance of ± 10%. Use a 10 Vpp sine wave at 1 kHz as the input signal to test the circuit. Before constructing the circuit use Spice to verify that both the max/min output voltage limits and the voltage gain from the input to Vo is as expected. Then construct the circuit and measure these values. 6. Voltage reference circuit using a Zener diode If the reverse bias voltage across a diode is increased to too large of a value, then the diode will eventually “break down” and conduct current in the reverse direction. This is not inherently destructive to the diode, as long as the current flowing through the diode is limited (usually with a series resistor) so that the power dissipated by the diode doesn’t exceed its maximum specification. The reverse bias breakdown voltage of a diode can be carefully controlled during its manufacture to create an exact value suitable for use as a reference voltage. This type of diode is called a “Zener diode”, and has the special symbol shown in Figure 6. Zener diodes are often used to create voltage references that can be used to set the value of other voltages, for example the output voltage of a variable power supply. Design the circuit in Figure 6. to create a reference voltage Use the +5V and -5V power supplies available on the Digilent Analog Discovery 2 to set the input voltage Vi to +10V. Then set the output reference voltage of this circuit to be +6.2V above the -5V supply voltage. Choose the value of the resistor R to set the reverse bias diode current Id = 1mA ± 10%. Before constructing the circuit use Spice to verify that both the output voltage and diode current are as expected. Then construct the circuit and measure these values. Also vary the input voltage Vi from +5V to +10V and measure the change in both the output reference voltage and diode current. Do this first in Spice, and then on the circuit you built on your breadboard. Add a Light Emitting Diode (LED) in series with the reference voltage Add a LED in series with the Zener diode in the circuit in Figure 6., to give a visual indication that current is flowing and the reference voltage is on and available for use. Vary the value of R to make the light from the LED brighter and dimmer by varying the current, but don’t allow Id to exceed 10mA.
Figure 6.