PHYSICS 338 Analog Electronics Laboratory Manual Fall 2011 Mods C&D Dr. Adam T. Whitten

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1 PHYSICS 338 Analog Electronics Laboratory Manual Fall 20 Mods C&D Dr. Adam T. Whitten

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3 Physics 338 Analog Electronics Lab Manual Fall 20 Preliminaries In Physics 200 you learned how to use digital multimeters (DMMs), oscilloscopes, and function generators. There will not be enough time in class or lab to review the fundamental operating procedures for these devices, so if you feel you need a refresher on their operation you can download the Electrical Measurements document at electric measurement.pdf and follow the tutorial before starting lab. For this lab course we will adopt the most common wire color coding convention for analog circuitry: black wires are used for 0 V ground connections red wires are used for 5 V power connections yellow wires are used for 5-5 V power connections blue wires are used for 5-5 V power connections any other color wire is used for signal connections Note: for analog household wiring (20 V, 60 Hz) black is power and white is ground. You will be using digital/analog protoboards in lab to build and test circuit. Improper connections can cause components to overheat and burn. This costs money, stinks up the lab room, and releases toxic materials into the air it is always a good idea to double check your connections before powering on the protoboard. Always use the Wavetek function generators, not the function generators built into the protoboards. The potentiometer (a.k.a. pot or variable resistor) is the most common item on the protoboard to be destroyed by students. A pot consists of a sweeper arm (denoted by the arrow) that touches a resistive slab at an adjustable location, dividing the resistive slab into two resistors. If the ends of the pot are connected to power and ground (see right), the sweeper samples the voltage in between the the ends. Pots are labeled with the total slab resistance R R 2, but individual values R and R 2 are in general unknown. On the protoboard, the sweeper is connected to the central four holes. If power and ground are accidentally connected between the sweeper and an end, then a huge current will flow when the knob is rotated to small resistances this burns off the delicate sweeper end. Never draw appreciable current from a sweeper! Lab Write-ups Your lab grade will be based on what you record in your Roaring Spring 5x5 quadrille ruled (or equivalent) lab notebook. Please be thorough, complete, and legible! Your lab write-ups for this course will be different from other courses you have taken and will be more informal. You should include the following items:. The title of lab. 2. A brief summary of the goals of the lab (2-4 sentences) 3. A parts list of components used which indicates actual number and type (i.e., 2N3906 pnp bipolar junction transistor, LF4 opamp). Note: Leave extra space to record additional

4 chips as required. Also include a listing of capacitor, inductor, and resistor values as well as any diodes (including type) used. Note: this list may change as you work on your circuit. 4. Clear and legible drawings of circuit diagrams as you encounter them in the lab manual. Identify each component using appropriate logic symbols with pins labeled and numbered. For transistors you do not need to number the pins, but be sure to label them. Note the symbols used for power depend on the component s fabrication technology bipolar junction transistors use V CC for the positive supply and V EE for the negative supply, whereas junction field effect transistors use V DD for the positive supply and V SS for the negative supply 5. Clear timing diagrams/drawings of oscilloscope traces when asked. Use the quadrille rules to line up timing events and make sure to label axes and scales. 6. Make sure to answer all questions as they are encountered in the lab manual. 7. A final reflective paragraph on what you learned should be included at the end. Lab notebooks are due on 3 days after your scheduled lab period at the beginning of class. 2

5 Physics 27A LAB Fall 20 AC Circuits, Impedance, and Filters Introduction and Pre-Lab In this lab you will investigate RC and RLC circuits. You will measure a RC time constant, examine the behavior of low-pass filter/integrator, examine the behavior of a high-pass filter/differentiator, and investigate the operation of band-pass and notch filters. Horowitz & Hill pages detail the generalization of resistance R to impedance Z for alternating current (AC) circuits. When the voltage varies sinusoidally with frequency f (ω = 2πf) we can write the voltage as: V = V 0 cos(ωt ϕ) = Re (V 0 e jϕ e jωt) = Re ( Ve jωt) where V = a jb is a complex number with magnitude V 0 and phase ϕ: a = V 0 cos ϕ = Re(V) b = V 0 sin ϕ = Im(V) V 0 = a 2 b 2 = V = (V V ) /2 tan ϕ = b/a Ohm s Law now becomes V = IZ (Z is the impedance) which means that V = I Z and that the phase of Z corresponds to the phase difference between V and I. Each of our passive components has an impedance which can introduce a phase shift and may have a frequency dependence. These are summarized in the following table: Component Impedance Phase Shift Frequency Dependence resistor Z R = R none constant capacitor Z C = j/ωc voltage lags current large/small at low/high frequency inductor Z L = jωl voltage leads current small/large at low/high frequency These characteristics allow us to construct some simple filters. Low-Pass Filter/Integrator The figure to the right depicts a RC low-pass filter or integrator. The name used to describe it depends on whether you are interested in the time domain response (integrator) or frequency domain response (filter). However, in order to be a good integrator only frequencies much greater than f 3dB should be applied. R C V The analysis is straight-forward for this voltage divider: I = = Z tot R (j/ωc) = V R (j/ωc) in R 2 /ω 2 C 2 ( ) R (j/ωc) j jrωc V = IZ C = R 2 /ω 2 C 2 = ωc ω 2 R 2 C 2 To get the amplitude, find the absolute value by multiplying by the complex conjugate and taking the square root: V = ω 2 R 2 C = V 2 in ω 2 /ω 2 ω = RC 3

6 To see that this is an integrator, consider a step function applied to the input at time t = 0. Note that V when ω ω and we can then write: I = C dv dt = V = V (t) = t dt constant R R RC Since the phase of is arbitrary, it can be taken as a real function giving a phase for V of: High-Pass Filter/Differentiator tan ϕ = Im(V) Re(V) = ωrc = ωrc The figure to the right depicts a RC high-pass filter or differentiator. The name used to describe it depends on whether you are interested in the time domain response (differentiator) or frequency domain response (filter). However, in order to be a good differentiator only frequencies much less than f 3dB should be applied. C R V Again the analysis is straight-forward for this voltage divider (I was calculated previously): V = IZ R = R (j/ωc) R 2 /ω 2 C 2 R = V = /ω 2 R 2 C 2 = ω 2 /ω 2 ω = RC To see that this is a differentiator, consider a step function applied to the input at time t = 0. Note that V when ω ω and we can then write: I = V R = C d dt ( V ) C d dt Again the phase of is arbitrary, so the phase of V is: Band-Pass and Notch Filters tan ϕ = Im(V) Re(V) = /ωc R = ωrc = V = RC d dt The simplest single pole band-pass and notch filters are shown in the figure below. In practice more than one pole is used, but working with single poles will allow you to investigate their behavior. R R C L V L V C Band-pass These get analyzed just like any other voltage divider only now there is either a parallel or series combination of L and C. Let Z eff be the effective impedance of the inductor and capacitor combination. For the band-pass filter (parallel configuration): Z eff = j/ωc jωl = jωc j/ωl = Z eff = 4 Notch j /ωl ωc = ja A = /ωl ωc

7 and write R/A as: V = Z eff R Z eff = ja R ja = V = R 2 /A 2 R A = R ωl ωrc = ω 2 ω ω ω ω 2 = R L ω = RC which means that for ω ω or for ω ω 2 the output V and V = when ω 0 = / LC. For the notch filter (series configuration): and write R/B as: V = R B = Z eff = jωl Z eff R Z eff = j ωc = jb B = ωl ωc jb R jb = V = R 2 /B 2 ( R ωl /ωc = ω ωl/r /ωrc = ω ) ω 2 ω which means that for ω ω or for ω ω 2 the output V and V = 0 when ω 0 = / LC. Note that for both filters the phase ϕ depends on the sign of A or B. Experiment. RC Time Constant Measurement Construct a low-pass filter circuit using R = 0 kω and C = 0.0 µf and drive it with a 500 Hz square wave. The time constant for discharging (or charging) τ = RC and can be measured on an oscilloscope by noting how long it takes the voltage V to fall to V 0 e from its maximum value. Display both and V on the oscilloscope and make a sketch of it in your lab notebook. Measure τ and compare it to the product RC. Next vary the frequency of up to 00 khz and sketch/describe how the output s magnitude and shape changes. What is the circuit s input impedance at dc (f = 0 Hz) and infinite frequency? 2. RC Integrator An input frequency of 00 khz is much greater than f 3dB = (2πRC), so you are in the range of frequencies where the circuit behaves like an integrator. Demonstrate that this is true by sketching input and output waveforms for all the different types of waveforms available on the function generator. 3. Low-pass Filter Calculate your circuit s 3dB frequency (i.e., for f 3dB, V = / 2) and verify this value experimentally with a sine wave input. Set the amplitude of your input sine wave to V and collect data on attenuation (V/ ) and phase shift (ϕ = 2π t/t ) over a range of frequencies f/f 3dB = 0., 0.2, 0.5,, 2, 5, 0, 20, 50, 00. Displaying V and simultaneously on the scope allows you to measure the lag/lead time t. Measuring the amplitudes and period, T, is straight-forward. Use the log-log graph paper provided to make a Bode plot of attenuation vs. frequency (i.e., log(attenuation) vs. log(f/f 3dB )) and check that the slope for f f 3dB is 20dB/decade (or 6dB/octave). Attach this plot in your lab notebook. Plot ϕ vs. f in your lab notebook and verify that the phase shift at f 3dB is as expected. Does V lag or lead? 5

8 4. High-pass Filter Reconfigure your R and C components to form a high-pass filter. Measure f 3dB and compare it with the expected value calculated from your component values. Collect attenuation and phase shift data for f/f 3dB = 0.0, 0.02, 0.05, 0., 0.2, 0.5,.0, 2.0, 5.0, 0. Use the loglog graph paper provided to make a Bode plot of attenuation vs. frequency and check that the slope for f f 3dB is 20dB/decade (or 6dB/octave). Attach this plot in your lab notebook. Plot ϕ vs. f in your lab notebook and verify that the phase shift at f 3dB is as expected. Does V lag or lead? 5. RC Differentiator Change your resistor and capacitor components so that R = 00 Ω and C = 00 pf. What is this circuit s f 3dB? Drive the circuit with a 00 khz triangle wave and show that it behaves as a differentiator by sketching the input and output waveforms in your lab notebook. Verify the differentiation behavior for all the other types of waveforms available on the function generator by sketching the input and output signals. 6. Band-pass Filter Construct a band-pass filter with R = 0 kω, C = 0.0 µf, and L = 0 mh. Calculate f 0, f, and f 2 for your circuit (recall ω = 2πf). Using a unit amplitude sine wave as the input, measure the output voltage over an appropriate range of frequencies and sketch the resonance curve V vs. f. Is the maximum response at the frequency you expect given the component values? Explain. Does the phase change, ϕ, over your range of frequencies correspond to what you expect? Explain. 7. Notch Filter Reconfigure your circuit to make a notch filter. Measure the output voltage over an appropriate range of frequencies and sketch the resonance curve V vs. f. Is the minimum response at the frequency you expect given the component values? Explain. Does the phase change, ϕ, over your range of frequencies correspond to what you expect? Explain. 6

9 Physics 27A LAB 2 Fall 20 Diodes and Power Supplies Introduction and Pre-Lab In this lab you will investigate the conversion of alternating current (AC) to direct current (DC), power supply regulation, diode clamping, and two new scope modes (differential and xy). Horowitz & Hill pages describe diodes and some of their practical applications. Rectification is the process of converting AC to DC. Diodes first convert ±V swings to positive voltage variations. A storage capacitor is then used to smooth out the variations in voltage. The smoothing is not perfect, however, and the resultant DC voltage has a ripple V associated with it. V = (I/C) t and is roughly a sawtooth wave, so the resulting rms voltage is ( V is a peak-to-peak value): V rms = V 2 3 = I t 2 3C For a full-wave rectifier, both the positive and negative portions of the input sine wave are used (pictured above) so t = /f. For a half-wave rectifier, only the positive portion of the input sine wave is used so t = 2/f. Note that the rms voltage depends on how much current is being drawn from the rectifier circuit. The term dc droop refers to the reduction in dc voltage due to current draw and it is 2 V. If the rectification circuit has no resistance (not a valid assumption) then the dc droop would be (I/2C) t. A common power supply specification is the load regulation, which is the maximum amount of dc droop usually expressed as a percentage of the designed output voltage V 0. The load regulation therefore depends on the maximum designed output current. Experiment V dc = V 0 V 2 = V 0 I t 2C. Half-wave Rectifier Construct the circuit shown to the right using a 7 V rms transformer and a A diode. Use various power resistors, making sure to keep I 0.5 A. Suggested values are R = 0, 20, 50, 00, 200 Ω. Sketch the output waveform for one of the resistors as seen on the scope with and without the capacitor. What value should you use for t? Use the one DMM to measure the voltage (Keithley preferred because of its smaller uncertainty) and a second DMM to measure the current (Metex is okay). For each of your power resistors measure the current I drawn by the load, the dc output voltage V dc, and the rms ac ripple voltage V rip. Use WAPP to fit and plot V rip vs. I and V dc vs. I. Because your rectifier has a non-zero output impedance, your may have to fit V dc to a quadratic expression. Calculate the effective capacitance of your rectifier from the appropriate fit value obtained from the V rip fit. Use your fits to calculate the ripple and load regulation at I = 4 A. If you double the capacitance, your ripple should be cut in half. Double your capacitance by adding another capacitor and note the effect when you have a 50 Ω power resistor in place. 7

10 2. Full-wave Rectifier Build either the bridge rectifier or the center-tapped rectifier. Make the same measurements, fits, and plots as you did for the half-wave rectifier. What value should you use for t? Compare the full-wave rectifier s ripple and regulation to the half-wave rectifier s ripple and regulation. Do they compare as expected according to the theory? 3. Power Supply Regulation Regulators are ICs that reduce the ripple and regulation. Insert a 7805 in between the capacitor and load of your full-wave rectifier circuit as shown to the right. Keeping I 4 A, measure the ripple and regulation and compare them with the unregulated circuit. Check the output on a scope to make sure there are no unwanted oscillations. Fits and plots are not necessary for the regulated circuit. Why? 4. Diode Clamp Construct the diode clamp circuit shown to the right and drive it with a khz large amplitude ( 0 V) sine wave. Sketch and your lab notebook and discuss the output. Make a voltage divider from kω and 2 kω resistors and divide the 5 V source to make a 5 V source. Sketch and your lab notebook for this new diode clamp and compare it with the previous diode clamp using the protoboard s 5 V source. Why is the signal less well clamped with the new 5 V source? What is the input impedance of each of the 5 V sources? (Hint: Apply Thèvenin s theorem.) Modify your new 5 V source by add a 6.8 µf bypass capacitor from the divider point to ground. What is the capacitor s effect on clamping? Discuss its operation. 5. Scope Differential Mode Construct the ac bridge circuit shown to the right to measure the resstance of a thermistor. Make R = 0 kω and use a variable resistance box for R A. When R A is equal to the resistance of the thermistor, the the voltages at x and y are the same this is called a null detector. Connect scope channels & 2 to x & y and put the scope into x minus y mode (i.e., in the math menu Operation ). Both channels should be set to the same scale (VOLTS/DIV). When the math menu is selected the scale for the math trace is set by the multipurpose knob and the selected value is displayed as the bottom option in the math menu. Using a 00 khz sine wave to power the bridge, adjust R A to get a null (i.e., 0 V difference between x and y) to get one value for the thermistor s resistance. Note that if the temperature of the thermistor changes (pinch it with your thumb and forefinger), you will no longer have a null reading. Measure the thermistor s resistance with an ohmmeter and compare the two results. Differential mode is useful for measuring the voltage across components in a live circuit when you can not apply a ground, but the finite resolution of the scope s ADC makes null readings suspect. 8

11 6. xy Mode Construct the circuit shown to the right which plots on the scope the current through a device (y) vs. the voltage across it (x). The scope must be in xy mode (in the display menu choose Format XY). Use a 60 Hz sine wave from the transformer to drive the circuit so you can set the ground to be between the device and the R = kω resistor. x (CH) is the voltage drop across the device and y (CH2) will be proportional to the current through the device (V = IR). You get positive y-values for positive currents by inverting CH2 (on the ch2 menu select Invert On). Observe the I V characteristics of a 00 Ω resistor, a Si diode, a Ge diode, and a Si zener diode. Sketch the curves obtained, record the scope s settings, and explain each element s behavior. What are the turn on voltages for the Si and Ge diodes? What is the zener (breakdown) voltage for the Si zener diode? 9

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13 Physics 338 LAB 3 Fall 20 Bipolar Junction Transistors Introduction and Pre-Lab Characteristic Curves and Load Lines The below figure shows the characteristic curves for a bipolar junction transistor (BJT) along with the load line for the simple common-emitter amplifier (R E = 0). What is the collector resisitor value, R C, and supply voltage, V CC, implied by this load line? Focus on the operating point Q for a base current of I B = 20 µa. Note that the collector current I C at this operating point is about 2.7 ma. Recall that the current gain β = h fe is: h fe = I C I C I B I B VCE =const = 2.7 ma.2 ma 20 µa 0 µa = 50 where.2 ma comes from where the dashed line intersects the 0 µa curve. If a signal input swings the base current by ±0 µa (indicated by the dotted lines), then the collector-to-emitter voltage V CE will have a range of about 7. ± 4.3 V. While the current gain is known to be β = 50, the voltage gain G V = / = V C / V B depends in the input impedance. Therefore, we would like to know what input voltage swing will cause the base current to change by ±0 µa. The base-emitter resistance r e depends on the collector current as derived from the Ebers-Moll equation: r e = (kt/q) I C 25 mv I C (ma) = 25 Ω for I C in ma I C For the operating point Q, I C = 2.7 ma giving r e = 9.3 Ω. The input impedance is then approximately Z in βr e = (50)(9.3 Ω) =.4 kω. Finally G V can be calculated: V C = I C R C = β I B R C = β V B Z in R C = V B βr C βr e = G V = V C V B = R C r e 300 Verify this voltage gain by calculating it to 2 significant digits using you derived collector resistor value R C from above. Remember that common-emitter amplifiers with R E = 0 suffer from non-linearity and varying Z in making them difficult to bias, so we should always use an emitter degeneration circuit with R E 0. 2N3904 Transistor Characteristic Curve with Load Line V CC Ic (A) µa Q 20 µa I C R C µa V B I B Vce (V)

14 Biasing and Blocking Capacitors The grounded common-emitter amplifier under consideration requires a base current of 20 µa to set the operating point Q. This is accomplished by using a voltage divider to set the base voltage V B one diode drop above the emitter voltage V E (in this case V E = 0). This is called biasing the transistor to set up its quiescent state. In this particular example V B 0.6 V and V C 7. V in the quiescent state. When signals are applied to the base, they must have any dc components removed so as not to alter this quiescent state. Therefore blocking capacitors are required to couple ac signals to the transistor. The choice of capacitance value depends mostly on the impedance of the voltage divider used to bias the transistor, Z div, and may depend on the input impedance of the transistor Z in (also called h ie in datasheets). In order to minimize the effects of Z in, make Z div 0Z in. For this particular circuit Z in =.4 kω, so make Z div 5 kω. The blocking capacitor then forms a high pass filter with Z div with a low frequency f 3db = (2πRC). Assume you make Z div = 9 kω. What minimum value of C is required to pass frequencies above 20 Hz? Measuring Input and Output Impedances To measure an input impedance you place a variable resistor between the signal source and the amplifier input and to measure an output impedance you use a resistor from the output to ground. In both cases the test resistor is adjusted until 2 the original output is achieved. The test resistances must not affect the biasing, so blocking capacitors must be placed in series with the test resistor in both cases. The input is always capacitively coupled and this capacitor appears in the circuit diagrams, but you must add a blocking capacitor to the output when measuring the output impedance. If the output impedance is small, a large ( 6.8 µf electrolytic) blocking capacitor is needed. In addition, a small output impedance allows large output powers, so power resistors are needed to measure the output impedance. Experiment. BJT Characteristics Select two 2N3904 npn BJT s and generate characteristic curves for each using the curve-tracing program available at keeping track of which plot corresponds to which device. From your characteristic curves determine the current gain h fe = β. Also use the Metex DMM to measure β. How do your measurements compare with each other and with the manufacturer s datasheet value of ? 2. Current Gain The current gain of a transistor depends on temperature and can vary from transistor to transistor of the same type. Therefore, a circuit that relies on a particular value of β is an unreliable circuit. Construct the circuit to the right in order to measure the current gain of one of your transistors. You will need to measure collector current I C and base current I B to find β = h F E. Use a large range for I B : µa to 0.3 ma. (Note: to keep I B < 0.3 ma, R B > 50 kω. Explain why.) Calculate the current gain β = I C /I B for each data point. The circuit limits the maximum value of I C. What is the theoretical value of I C,max for this circuit? Make a log-log plot of β vs. I C using and compare the results with those of part. Is β a constant? R B A 5V I B 2N 3904 E B C I C A 2N 3906 E B C 470Ω 2

15 3. Emitter Follower Construct the emitter follower circuit shown to the right, drive it with a 0 khz sine wave, and simultaneously observe the input and output waveforms on an oscilloscope. What is the ac gain? Measure the base and emitter dc bias voltages and comment on whether or not they are what you expect them to be. Measure the amplifier s input impedance and compare it with your theoretical expectation. Using the power resistor set (0, 20, 50, 00, 200 Ω) from the power supply lab and a 6.8 µf blocking capacitor, estimate the output impedance. Is it what you expect? 30k µf 50k 5V R R 2 R E 7.5k 4. Common-Emitter Amplifier Construct the common-emitter amplifier circuit shown to the right. Measure the ac voltage gain, input impedance, and output impedance. Compare these values with the theoretical values (which you must calculate). Measure the high frequency f 3dB point. Now bypass the emitter resistor R E with a 6.8 µf electrolytic capacitor and again measure the ac gain. How does it compare with the theoretical value? Note: with C E present you will have to keep the amplitude of the input signal small to avoid clipping. 30k µf 5k 5V R R C R 2 R E 6.8k 680Ω C E 5. Complementary Push-Pull Follower This circuit is the basis for the output stage of most audio power amplifiers. Construct it, drive it with a large amplitude sine wave, and observe the crossover distortion in as you change both the amplitude and dc offset of. Sketch the input and output when the input amplitude is about 2 V p-p with zero dc offset. Explain your observations. For zero dc offset in, is crossover distortion more of a problem for small or large input amplitudes? 5V npn pnp 5V 6.8k 3

16 6. Differential Amplifier: long-tailed pair Using a matched pair (note: only matched in β, not thermal characteristics) of 2N3904s, construct the circuit shown on the left below. One input (V ) is a non-inverting input and the other input (V ) is an inverting input. Measure the circuit s differential gain by grounding one input and applying a small signal to the other input. Measure its common-mode gain by driving both inputs with the same V p-p sine wave. From these data compute the commonmode rejection ratio (CMRR =, diff /,CM ) and compare with the theoretical values given by H&H section 2.8: G diff = R C 2(R E r e ) R C G CM = CMRR R tail 2R tail R E r e R E r e Save this circuit for part 7! 7. Current Mirror: active tail Construct the current mirror shown on the right below and report/explain the formula relating the programming resistor R p to the constant current I. (Select R so that about 0.- V drops across it for currents of a few ma e.g., 200 Ω.) Check whether I I p (as would be expected for identical transistors). Over what range of R x is the current approximately constant? Try a second value for R p and again measure both I p and I. Discuss what determines the range of R x values over which this circuit is useful. Finally remove the portions of the current mirror and differential amplifier circuits in the dashed boxes and substitute the current mirror for the long tail of the differential amp. Measure the differential amp s new differential and common-mode gains and compare the CMRR with its previous value from part 6. 5V µf R C 7.5k µf R x A for testing purposes R p I p 7.5k V 0k R B R E 00Ω R E 00Ω R B 0k V constant current sink: I 7.5k R tail R R 5V "long tail" Circuit for Part 6 5V Circuit for Part 7 4

17 Physics 338 LAB 4 Fall 20 Operational Amplifiers Introduction and Pre-Lab The Golden Rules. The output attempts to do whatever it can to make the voltage difference between the inputs zero. 2. The inputs draw no current inputs { 5 V CC k V EE In this lab you will investigate several common op-amp circuits using the LF4 op-amp. Before you come to lab, design an inverting amplifier with a gain of 0 using an op-amp and reasonable values for the input and feedback resistors (i.e., kω-00 kω). Experiment. Open-loop Test Circuit Construct the open-loop test circuit to the right and observe the output on an oscilloscope set to 5 volts/div. What happens as you slowly turn the potentiometer? Is it possible to measure the open-loop voltage gain? Provide evidence for a statement of the form the gain must be greater than X. (Hint: if the gain were 0 6 and = V is desired, calculate the required and simply adjust the potentiometer to get that voltage.) 0k 5V 5V 0k V 5V V 6 2. Inverting Amplifier Construct the non-inverting amplifier you designed for the pre-lab. Drive your amplifier with a khz sine wave and measure its small-signal gain by observing the input and output waveforms on the oscilloscope. Does the gain depend on the input amplitude? What is the maximum output voltage swing? Sketch an oscilloscope trace showing output clipping (include scope settings). Measure the gain at different frequencies: what is an approximate upper frequency limit (f 3dB, where has been reduce by a factor of 2 )? Measure the slew rate (maximum time rate of change of the output voltage) in V/µs using a high frequency, large amplitude square wave as the input by observing the rising/falling edge of the output on the oscilloscope. Compare with the manufacturer s specs. 3. Non-inverting Amplifier Construct a non-inverting amplifier using the same components as in part 2. Measure its voltage gain and compare with the theoretical value. 5

18 5V 4. Current Source Construct the op-amp current source shown to the right. Vary the load resistor R L (you may use the variable resistor box) and monitor the current: over what resistance range does the current remain constant? (If the current isn t constant for small R L, check the op-amp for oscillations.) Calculate what the theoretical current should be and compare with your measurements. Why does the current not remain constant at large R L? 5k k 5V 5V 80Ω A R L 5. Summing Amplifier The inverting op-amp configuration in conjunction with summing inputs can be used as a digital-to-analog converter. The four input bits of the binary (base 2) number (e.g., 0 2 = 3 0 ) have voltages of either 0 V for 0 or 5 V for. The resistors are chosen to weight the bits appropriately according to whether they are in the s, 2s, 4s, or 8s place (s place is given the least weight). Construct this circuit and measure the output voltage with a DMM for all 6 possible binary inputs. Plot and fit vs. digital input and find the fit parameters. Are the fit parameters what you expect from a theoretical analysis of the circuit? kΩ 3.9kΩ 2.0kΩ.0kΩ.0kΩ 5V 5V 6. Integrator Construct the integrator shown. Drive it with a khz sine wave and observe the output on an oscilloscope (dc coupled) while varying the dc offset of the input signal. Describe what you observe. (Note: even if the function generator s dc offset is off, there will be a small dc offset in the output signal!) What is the function of the 0 MΩ resistor? (Remove it and see what happens, but then replace it.) Draw oscilloscope traces showing input and output for all three of the available waveforms on the function generator. To observe the output waveform you may need to switch Coupling AC to remove the dc offset, allowing you to switch to an appropriate volts/div scale. Is d dt? Measure the input offset voltage with a DMM. Is it within specs? Use the trimming circuit shown in the introduction to zero out the offset voltage. Describe the effect of this on the integrator output. 00kΩ 0MΩ 0.0µF 5V 5V 6

19 Physics 338 LAB 5 Fall 20 Field Effect Transistors Introduction and Pre-Lab Characteristic Curves and Load Lines The characteristic curves for a JFET along with a load line for the circuit of part 2 are displayed below. Report the value of R D for this loadline! An operating point (a.k.a. quiescent point) Q has been selected at a gate bias voltage V GS = 0.4 V and drain current I D.7 ma. The transconductance g (a.k.a. forward admittance y fs ) at Q is given by: g = I D I D 2.2 ma. ma = = 2.8 ms V GS 0.2 V 0.6 V V GS VDS =constant The SI unit of transconductance is siemens (S) and is equivalent to Ω. In some texts and professions the non-si unit mho ( ) is still used. If an input voltage swings the gate voltage ±0.2 V, the drain-to-source voltage V DS voltage range will be about 6.7 ± 2.8 V giving use a gain of about 4. Note that a FET with a different set of characteristics curves would in general give us a different gain. Using a larger value of R D would force us to small I D operating points and lower regions of transconductance since more closely spaced characteristic curves mean lower g explain why! On the other hand, smaller drain resistors with their more steeply sloped load lines gives us small V DS swings, but push us to operating points nearer to the V DD = 5 V rail. The gain could be maximized if we had a nearly flat load line (e.g., a current source that always sources.7 ma, independent of the voltage across it). Note that with such a flat load line through Q a swing in V G < 0. V swings V DS nearly rail-to-rail N5457 JFET Characteristic Curve with Load Line V ID(A) Q 0.4V 0.6V 2N 5457 D S G 2N 5460 D S G V DS (V) Experiment. FET Characteristics Select two different 2N5457 n-channel JFETs and obtain characteristic curves for each using the web-based curve tracer ( Keep track of which characteristic curves correspond to which device! Call the JFET with the larger I DSS FET A and the other one FET B. 7

20 Reading off the characteristic curve plot for FET A, make a table of I D vs. V G at V DS = 7.5 V. According to H&H you should find: I D = k(v G V T ) 2 = kv 2 G 2kV G V T kv 2 T }{{} theoretical form = AV 2 G BV G C }{{} fit form where V T is the threshold voltage and k is determined by the FETs s geometry, which both vary from device to device. Fit your data to a quadratic function and plot it (attach both the fit results and the plot in your lab notebook). Calculate the derivative of your fit and note that this slope (of the I D vs. V G plot) is the transconductance g (a.k.a. y fs ). Use the fact that the slope should be zero at V G = V T to calculate V T from the fit s derivative. Since the derivative of a quadratic is linear, g increases linearly for V G (V T, 0 ). Calculate y fs at V G = 0. Compare your values of I DSS, V T, and y fs to the spec sheet values. Note that the derivative of your fit is: I D = 2kV G 2kV T = 2AV V G }{{} G B }{{} theoretical form fit form 2. FET Voltage Amplifier Construct the amplifier shown to the right using FET A. Determine R D by selecting a resistor that makes a nice load line on FET A s characteristic curves. Add the load line to your characteristic curves plot. Select and label your operating (quiescent) point Q. Use the dc offset of your function generator to bias the gate (initially with only a dc signal) to your operating point. Measure the output voltage as you change this dc bias. Plot the resulting points on your characteristic curve (they should lie near the load line). 4.7kΩ R D 5V Now switch to a sine wave with a dc offset. Again monitor on your scope as you vary the dc bias and record both the lower and upper levels of dc offset that result in clipping of. Return the bias level so that you are back near your Q operating point. Keeping the input amplitude small enough to avoid clipping, measure the ac voltage gain v out /v in at a frequency of 0 khz (recall that lower case letters indicate the ac component only). Compare your result with the approximate theoretical value G V = gr D. (This requires you to find g at Q.) Vary the input frequency through several decades and note that gain is approximately constant throughout a large bandwidth. Find the high frequency f 3dB. Save this circuit for part 4! 3. FET Current Source Construct the amplifier shown to the right using FET B. Initially short the gate and source (i.e., R S = 0) and measure the current with varying load R L. Over what range of R L is the current approximately constant? How does this relate to the V G = 0 characteristic curve? A 5V R L Consider the case of non-zero R S. Using your characteristic curves, pick a nice value of I D and the corresponding V GS. Calculate the required R S and build the circuit. How does the experimental constant current value compare to the design value? Save this circuit for part 4! R S 8

21 4. Active Load In the pre-lab it was noted that the best possible load for a FET amplifier is a constant current source. You ve constructed a voltage amplifier using FET A in part 2 and a constant current source using FET B in part 3. Now put the two together using the gate-shorted-to-source version of the current source shown to the right. Find and report the gate bias voltage (for FET A) needed to maximize the small signal gain of this amplifier. Report that maximum gain and compare it to the gain from part kΩ 5V Recall that if you really want voltage gain, FETs are not the device to use an LF4 can produce gains of Voltage-Controlled Gain Amplifier This circuit uses FET A as a voltage-variable resistor (VVR). The aim is to construct an amplifier whose gain is controlled by a dc voltage on the FET s gate, requiring the FET to operate in the ohmic (linear) region where V DS is small (e.g., small than the gate drive V G V T ). Explain why V DS = is expected. Construct this circuit using an LF4 and choosing R to be 40 the V G = 0 FET resistance (i.e., y fs ) found in part. Drive the circuit with an ac signal of about 5 khz and an amplitude small enough to avoid clipping (e.g., < 00 mv). Make a graph of voltage gain G V vs. the pot-controlled gate voltage V G. You should recognize the op amp as a non-inverting amplifier...write out the equation for its gain. Where is the second resistor R 2? Looking at your FET characteristic curves, what range does R 2 have? Operating at a fairly large negative control voltage (e.g., V T /2), see how much you can increase the input signal amplitude before the output waveform becomes distorted. Note the value of V DS when this distortion sets in and refer to your characteristic curves to explain its cause. This distortion can be decreased by adding the feedback elements shown between points A and B. Try this fix and note its effect. (See H&H p. 39 for a quantitative explanation.) Save this circuit for part 6! 5V A B 5V R 0kΩ 5V MΩ 0.0µF B MΩ A additional feedback components 9

22 6. Automatic Gain Control (AGC) The AGC circuit shown uses a voltage-controlled gain amplifier to keep nearly constant over a wide range of amplitudes for. These circuits are used in radios and tape recorders to maintain a constant volume output for input signals whose strength may vary considerably it is designed to boost the gain of low amplitude inputs. The AVLS (automatic volume limiting system) found on mp3 players and PlayStations is similar it is designed to reduce the gain of high amplitude inputs. Build this circuit from the amplifier of part 5 and demonstrate it to your instructor (the op amps should be connected to ±5 V power supplies). Measure the range of amplitudes for over which remains nearly constant. Note that when the circuit is regulating the gain, the potentiometer acts as the volume control. A duplicate of the circuit diagram below is included on the last page for you to cut and tape into your lab notebook. Do this and then circle and label the following parts of the circuit: () a non-inverting amp with a voltagecontrolled resistor, (2) a half-wave rectifier with a capacitor filter, and (3) an integrator with summing inputs. A former student commented, If the inputs to the integrator are constant, the output will also be constant. Is this a correct statement? Explain qualitatively how this circuit works as an AGC amp. Begin by answering the following questions. In part 5 you saw that the gate voltage determined the gain. Which part of this circuit controls the gate voltage? What is required for the gate voltage to remain constant? What condition forces a decreasing gate voltage? Assume that is too large so that the gain of the amplifier needs to be reduced. Report the chain of consequences that will cause the gate voltage to be correctly adjusted (up or down?) to bring about the required reduction in gain. If the potentiometer is adjusted so that its voltage becomes more negative, report the chain of consequences that will affect (up or down?) the gain. 0.0µF MΩ R 0.0µF Ge Ge 0kΩ 5V MΩ 0.0µF MΩ MΩ 20

23 Physics 338 LAB 6 Fall 20 Introduction and Pre-Lab Active Filters In this lab you will investigate voltage-controlled voltage-source (VCVS) active filters and state variable filters. State variable filters are more stable and are easier to adjust than VCVS filters. Three common filter types are the Butterworth, Chebyshev, and Bessel filters and each has its own advantages and disadvantages. Butterworth Advantages: Disadvantages: Chebyshev Advantages: Maximally flat magnitude response in the pass-band. Good all-around performance. Pulse response better than Chebyshev. Rate of attenuation better than Bessel. Some overshoot and ringing in step response. Poor phase characteristics. Better rate of attenuation beyond the pass-band than Butterworth. Disadvantages: Bessel Advantages: Disadvantages: Ripple in pass-band. Considerably more ringing in step response than Butterworth. Best step response very little overshoot or ringing. Best phase characteristics. Slower initial rate of attenuation beyond the pass-band than Butterworth. All filter types can be used to make low-pass, high-pass, band-pass, and band-reject filters. In theory, a band-pass filter can be made by cascading overlapping low- and high-pass filters and a band-reject can be made by summing the outputs of non-overlapping low- and high-pass filters, but there are better circuits available for these types of filters (see H&H Figs. 5.5 & 5.7). 2 pole VCVS filter circuits Controlled source filters use noninverting amplifiers with gains greater than. The difference between low-pass and high-pass filters is in the placement of the resistors and capacitors. R R 2 C V CC C C2 R V CC C 2 V EE (K)R R 2 V EE (K)R R R 2 pole VCVS low-pass filter 2 pole VCVS high-pass filter Choosing the proper resistor, capacitor, and K values is outlined in H&H Section

24 2 pole state-variable filter circuits State-variable filters usually come pre-packaged in a single IC with capacitors (C, C 2 ) and resistors (R, R 2, R 3, R 4 )preset to specific values. This requires that the user only needs to set resistor values R F,2, R G (gain resistor), and R Q (Q-factor resistor). There is usually software available from the manufacturer that calculates these resistor values for you. The input stage can be configured as an inverting amplifier. R 2 C R C2 R G V CC RF V CC RF2 V CC R Q V EE V EE V EE R 4 V highpass V bandpass V lowpass For Butterworth filters the high- and low-pass outputs have the same cutoff frequency, f c, for a given R F for Chebyshev and Bessel filters, different values of R F must be chosen to get equivalent f c s for high- and low-pass configurations. If the bandpass filter is desired, R Q must be reduced compared to the low- or high-pass values to increase the sharpness of the peak. The input stage can also be configured as a noninverting amplifier for bandpass filtering. R 2 R C C2 V CC RF V CC RF2 V CC R 3 V EE R 4 V EE V EE R Q Vhighpass V bandpass Vlowpass Again, if the bandpass filter is desired, R Q must be reduced compared to the low- or high-pass values to increase the sharpness of the peak. For a band-reject filter, use a reduced R Q and summing amplifier to combine the outputs of the first (high-pass) and third (low-pass) amplifiers. Experiment. Construct a 2 pole VCVS low-pass Butterworth filter with f c =.0 khz. Choose R = R 2 = 59 k and C = C 2 = 0.00 µf. Also set R = 00 k and (K )R = 58.6 k. These values were calculated from H&H Table 5.2. Set the amplitude of your input sine wave to V and collect data on attenuation (V/ ) and phase shift (ϕ = 2π t/t ) over a range of frequencies f/f c = 0., 0.2, 0.5,, 2, 5, 0, 20, 50, 00. Displaying V and simultaneously on the scope allows you to measure the lag/lead time t. Measuring the amplitudes and period, T, is straight-forward. Make a Bode plot of attenuation vs. frequency (i.e., log(attenuation) vs. log(f/f c )) using 22

25 the log-log graph paper provided, WAPP2PLOT, or Mathematica and attach this plot in your lab notebook. Plot ϕ vs. f using the semi-log graph paper provided, WAPP2PLOT, or Mathematica and attach this plot in your lab notebook. 2. Turn your VCVS low-pass Butterworth filter into a high-pass Butterworth filter by interchanging the appropriate resistors and capacitors. Keep the amplitude of your input sine wave at V and collect attenuation and phase shift data for f/f c = 0.0, 0.02, 0.05, 0., 0.2, 0.5,.0, 2.0, 5.0, 0. Make a Bode plot of attenuation vs. frequency and a plot of ϕ vs. f. Attach these plots in your lab notebook. 3. Construct a 2 pole VCVS low-pass Bessel filter with f c =.0 khz. Choose R = R 2 = 25 k and C = C 2 = 0.00 µf. Also set R = 00 k and (K )R = 26.8 k. These values were calculated from H&H Table 5.2. Keep the amplitude of your input sine wave at V and collect attenuation and phase shift data for f/f c = 0.0, 0.02, 0.05, 0., 0.2, 0.5,.0, 2.0, 5.0, 0. Make a Bode plot of attenuation vs. frequency and a plot of ϕ vs. f. Attach these plots in your lab notebook. 4. Turn your VCVS low-pass Bessel filter into a high-pass Bessel filter by interchanging the appropriate resistors and capacitors. Note that R and R 2 need to be changed to 203 k. Collect attenuation and phase shift data for f/f 3dB = 0.0, 0.02, 0.05, 0., 0.2, 0.5,.0, 2.0, 5.0, 0. Make a Bode plot of attenuation vs. frequency and a plot of ϕ vs. f. Attach these plots in your lab notebook. 5. Construct a 2 pole state-variable Butterworth inverting filter with f c =.0 khz. Set R = R 2 = R 4 = R G = 50.0 k, C = C 2 = 0.00 µf, R F = R F 2 = 58.0 k, and R Q = k. Set the amplitude of your input sine wave at V and collect attenuation and phase shift data for f/f c = 0.0, 0.02, 0.05, 0., 0.2, 0.5,.0, 2.0, 5.0, 0 for both the high- and low-pass outputs. Make a Bode plot of attenuation vs. frequency and a plot of ϕ vs. f. Attach these plots in your lab notebook. Qualitatively examine the bandpass output as you change the frequency through the range 0.0 f/f c 0 and record your observations in your lab notebook. Change the Q-factor resistor to R Q = k and collect attenuation and phase shift data for f/f c = 0.0, 0.02, 0.05, 0., 0.2, 0.5,.0, 2.0, 5.0, 0. Make a Bode plot of attenuation vs. frequency and a plot of ϕ vs. f. Attach these plots in your lab notebook. Questions. Compare your VCVS low-pass Butterworth and Bessel filters by examining their Bode and phase plots. Record your observations. Do they compare as expected? 2. Compare your VCVS low-pass Butterworth and Bessel filters by examining their Bode and phase plots. Record your observations. Do they compare as expected? 3. Compare your two low-pass Butterworth filters (VCVS and state-variable) by examining their Bode and phase plots. Record your observations. Do they compare as expected? 4. Compare your two high-pass Butterworth filters (VCVS and state-variable) by examining their Bode and phase plots. Record your observations. Do they compare as expected? 5. Comment on your state-variable bandpass filter by referring to its Bode and Phase plots. What is it s Q-factor? How does the phase change with frequency? 23

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27 0.0µF MΩ R 0.0µF Ge Ge 0kΩ 5V MΩ 0.0µF MΩ MΩ 25