* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Pre-Lab Work and Quiz - facstaff.bucknell.edu
Immunity-aware programming wikipedia , lookup
Analog-to-digital converter wikipedia , lookup
Crystal radio wikipedia , lookup
Index of electronics articles wikipedia , lookup
Integrating ADC wikipedia , lookup
Transistor–transistor logic wikipedia , lookup
Regenerative circuit wikipedia , lookup
Negative resistance wikipedia , lookup
Josephson voltage standard wikipedia , lookup
Nanofluidic circuitry wikipedia , lookup
Electrical ballast wikipedia , lookup
Power electronics wikipedia , lookup
Two-port network wikipedia , lookup
Operational amplifier wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Schmitt trigger wikipedia , lookup
RLC circuit wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Voltage regulator wikipedia , lookup
Power MOSFET wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Current source wikipedia , lookup
Surge protector wikipedia , lookup
Current mirror wikipedia , lookup
Rectiverter wikipedia , lookup
ELEC 350L Electronics I Laboratory Fall 2012 Lab #5: Digitally Controlled Attenuator – Part 2 Introduction Last week in Part 1 of this lab exercise, you designed a circuit to supply a variable voltage using a binary up/down counter and a multi-input scaling and level-shifting circuit. This week, you will design and assemble the attenuator circuit that will be controlled by the variable voltage supply. You will then test the complete attenuator system to verify that it can control the amplitude of a sinusoidal signal. Pre-Lab Work and Quiz Before arriving at the lab session, read over the “Theoretical Background” and “Experimental Procedure” sections of this handout carefully, and perform the calculations necessary to fill in the blank spaces in Table 1. At the beginning of the lab session, submit a completed table accompanied by a brief explanation (with equations) of how you calculated the required data. The pre-lab work may be handwritten on loose-leaf paper, and it will not be graded for style, formatting, spelling, and grammar. However, it must be legible and easy to follow. Theoretical Background Recall that the i-v characteristic of a pn-junction diode is described by the diode equation, i D I S e vD / nVT 1 , where, as shown in Figure 1, iD is the current flowing through the diode in the direction of the arrow in the circuit symbol, and vD is the diode voltage, which obeys the passive sign convention (i.e., iD flows into the positive side of vD). The constant IS is the reverse saturation current, and the constant n is the empirically determined emission coefficient, the value of which varies between one and two for most silicon diodes. The constant VT is the thermal voltage, given by VT kT T , q 11,600 where T is the temperature in kelvins; k is Boltzmann’s constant (1.38 × 1023 J/K); and q is the charge on a single proton (1.60 × 1019 C). At a temperature of approximately 293 K (20 C or 68 F), VT ≈ 25 mV. iD + vD − Figure 1. Definitions of diode current and diode voltage. Both quantities are positive if the diode is forward biased. 1 of 6 As we have seen, it can be difficult to solve circuit problems using the diode equation because of its nonlinear form. The piecewise linear (PWL) model of the diode has therefore been developed to approximate the i-v characteristic. Its circuit representation consists of linear circuit elements, specifically, an independent voltage source VF in series with a resistor rd. The i-v characteristic that corresponds to the PWL model is shown as a dashed line in Figure 2, and the actual i-v characteristic described by the diode equation is shown as a solid curve. The accuracy of the model depends on evaluating the slope of the curve near the operating point of the diode, the part of the curve associated with the expected current through (or voltage across) the diode during normal operation. The reciprocal of the slope is equal to the value of the “on” resistance rd, more commonly called the diode small-signal resistance or the incremental resistance. If the diode current fluctuates significantly, it might be pointless to determine the value of rd since it too would fluctuate. However, in a situation where the current varies only a small amount around an average value, the inclusion of rd in the diode model can be very helpful. As we shall see, it is central to the design of diode-based attenuators. iD slope = 1/rd vD VF Figure 2. Piecewise linear (PWL) representation of the i-v characteristic of a pnjunction diode. The PWL representation can be modeled as an independent voltage source of value VF (which represents the diode’s turn-on voltage) in series with a resistor of value rd. Many types of attenuator circuits use the internal resistances of one or more diodes as elements of a voltage divider (or more sophisticated voltage reduction circuits). A simple approach is illustrated in Figure 3. Resistor RB and control voltage VS are chosen to establish a “quiescent,” or average, DC current flowing through the diode. The time-varying signal coming from the function generator (represented by vg and Rg) is assumed to be weak enough so that the current it causes to flow through the diode is a tiny fraction of the DC current. Thus, the diode’s “on” resistance rd is not significantly affected by the signal current. The two capacitors C1 and C2 connected to the anode of the diode in Figure 3 are called DC blocking capacitors, and their purpose is to keep DC current from flowing anywhere but through the diode. If they have large enough values, they will pass AC signals easily. Recall that the reactance of a capacitor can be determined via XC 1 . 2 f C 2 of 6 C3 VS Function Generator Rg vg + − RB C1 C2 + vD − iD + vo − RL Figure 3. A simple diode-based attenuator. Resistor RB sets the DC component of the diode current, which in turn controls the diode’s “on” resistance rd. If RL >> rd and RB >> rd, then the effect of those two resistors can be ignored, and the on resistance can be assumed to form a voltage divider with the function generator’s output resistance Rg. The values of C1 and C2 are chosen so that their reactances are insignificant compared to Rg, rd, and RL at the lowest frequency of interest (where XC is greatest in magnitude). The capacitor C3 in parallel with the power supply VS ensures that any signal current that flows through resistor RB is shunted to ground in the vicinity of the circuit rather than flowing through the power supply circuitry. It is called a bypass capacitor. The relationship between the diode “on” resistance and the DC quiescent current is determined by taking the derivative with respect to vD of the diode equation for the special case when vD is large enough to satisfy the approximation i D I S e vD / nVT . This occurs when VD >> nVT, that is, when vD is greater than a few tenths of a volt. The derivative is 1 vD / nVT 1 di D e I S e vD / nVT . I S dv D nV nV T T Note that the second quantity in parentheses on the right-hand side is the diode current (to a very good approximation) under forward bias conditions. Thus, di D i D . dv D nVT The total current iD through the diode can be decomposed into its DC and AC parts as 3 of 6 i D I D id , where ID is the DC quiescent (constant) average current and id represents the time-varying component of the current (the AC variation). (This upper-case/ lower-case convention used to distinguish between purely DC and purely AC signals is widely used in textbooks and technical papers.) If the AC variation is small relative to the quiescent level (i.e., id << ID), then we can make the approximation iD ≈ ID. Substituting this approximation and the definition di D 1 dv D rd into the expression for diD/dvD found above yields rd nVT . ID The thermal voltage VT is well defined (if the temperature is known), but n is an empirically derived quantity. The value of n might be available on a datasheet, but more typically it must be determined by measurement. A circuit representation of the attenuator that is valid for small AC signals only is shown in Figure 4. Note that resistor RB is depicted as grounded on one side. This is because of the bypass capacitor in the actual circuit; it shorts one side of RB to ground with respect to AC signals. Also note that the turn-on voltage VF of the diode is not included because it is a DC independent source. It has no effect on the AC operation of the circuit. Employing an AC model like the one in Figure 4 is akin to applying the principle of superposition and evaluating only the contributions of the AC source (vg) to the voltages and currents in the circuit. All of the DC voltage sources have been replaced with short circuits, as have the low-reactance capacitors. Function Generator Rg vg + − rd RB + vo − RL Figure 4. AC representation of the attenuator circuit. Resistance Rg is the internal resistance (the output resistance or Thévenin equivalent resistance) of the signal source. The capacitors are not explicitly shown because they are assumed to be shorts at the AC signal frequency. If RL >> rd and RB >> rd, then the value of rd dominates the parallel combination of rd, RB, and RL. 4 of 6 Experimental Procedure Your task is to design and test an attenuator circuit like the one shown in Figure 3. The bench-top function generator, which has an output resistance Rg of 50 , will serve as the AC signal source. The generator voltage vg should be no more than approximately 100 mVpk to ensure that the signal current through the diode is small relative to the DC (quiescent) current. Remember: The amplitude displayed on the function generator’s screen is half the value of the Thévenin equivalent voltage vg. You may use a very high resistor value for RL (several hundred k, for example) so that the loading effect of RL can be ignored. Use a 1N914 or 1N4148 diode, and select a value for the DC blocking and AC bypass capacitors so that they have less than 1 of reactance at 1 kHz and above. You will most likely have to use electrolytic capacitors, so be sure to determine the proper orientation of each capacitor in the circuit. Your circuit should provide an attenuation setting of vo/vg = 0.10 when the control voltage (the output of the scaling and level-shifting circuit you designed last week) is at its maximum value of 11.75 V. When the control voltage is 0.5 V, there should be almost no attenuation (i.e., vo ≈ vg). Base your design on the assumptions that rd << RL and rd << RB and that the diode’s emission coefficient n is approximately 1.5. You will also need to assume a reasonable approximation for the diode’s turn-on voltage VF. Consult the appropriate data sheet for guidance. Also, remember to check the power dissipated by the various components. If a component might have to dissipate more than its rated power, you must devise a way to work around the problem. As part of your pre-lab work, you should have completed Table 1 with predicted attenuation settings for all 16 control voltages. Table 1. Attenuator specifications and operating parameters. The diode “on” resistance should be based on an assumed value for n of 1.5. Binary Decimal Control Quiescent Diode Diode “On” Attenuation Number Equivalent Voltage (V) Ratio (vo/vg) Current (A) Resistance () 0000 0 0.50 ≈ 1.00 0001 1 1.25 0010 2 2.00 0011 3 2.75 0100 4 3.50 0101 5 4.25 0110 6 5.00 0111 7 5.75 1000 8 6.50 1001 9 7.25 1010 10 8.00 1011 11 8.75 1100 12 9.50 1101 13 10.25 1110 14 11.00 1111 15 11.75 0.10 5 of 6 Assemble your attenuator circuit, and connect it to the variable voltage circuit you designed and built last week. Use the oscilloscope to verify that your circuit is providing close to the specified amount of attenuation at each control voltage setting. Try applying the “BW Lim” feature if there is a lot of noise on the trace. Do not rely on the automatic voltage readings displayed on the screen to record the various values of vo; the “fuzz” on the trace makes that feature useless. Use the manual cursors instead. [10 pts EXTRA CREDIT] If your results are consistently off in one direction for the higher control voltage settings, consider the possibility that the estimated value for the emission coefficient n that you assumed is incorrect. Devise a way to determine the value of n that results in the best agreement between your target and measured attenuation levels, and use the new value to revise your circuit design. Verify that your revised circuit is achieving the target attenuation levels more closely. Report your initial and revised measurements. Demonstrate your properly working circuit to the instructor or TA. Disagreements between target and measured attenuations that are attributable to the wrong assumed value for n are acceptable. Capture screen images of the output voltage waveforms for the highest, lowest, and middle (VS = 6.5 V, corresponding to binary 1000) attenuation settings to provide additional evidence that your circuit is working properly. Include the screen images in your report with appropriate discussions and any necessary annotations added. Be sure to include the value of vg you used. Grading Each group must submit a brief but well written report that describes in detail all circuit design choices, assembly steps, and the results of measurements. The report should include (but not necessarily be limited to) all of the details requested in the “Experimental Procedure” section. Pay especially close attention to the instructions and issues addressed in the “Lab Report Guidelines” available at the lab web site. Issues that are specifically addressed in the “Guidelines” will lead to larger grade penalties. The report is due at the beginning of next week’s lab session. Each group member will receive the same grade, which will be determined as follows: 10% 40% 30% 10% 10% Pre-lab work: Copy of Table 1 with all blanks filled in Demonstration of properly operating attenuator circuit Report – Completeness and technical accuracy Report – Organization, neatness, and style (professionalism) Report – Spelling, grammar, and punctuation © 2011-2012 David F. Kelley, Bucknell University, Lewisburg, PA 17837. 6 of 6