University of Pennsylvania Department of Electrical and Systems Engineering ESE319

Transcription

1 University of Pennsylvania Department of Electrical and Systems Engineering ESE39 Laboratory Experiment Parasitic Capacitance and Oscilloscope Loading This lab is designed to familiarize you with some of the capabilities and limitations of some of the equipment that we will be using in the course and to demonstrate some techniques we can use for circuit model simplification and approximation. It is important that you read and study the material contained in the document: Electronic Circuits - Modeling and Measurement Techniques before proceeding with the lab work.. Introduction. We will focus on the most important pieces of test equipment: A Hewlett-Packard function generator and arbitrary waveform generator that will be our primary source of stimulus signals for circuits under test. The Hewlett-Packard oscilloscope used to display the circuit s response to the function generator stimulus. The coaxial cable and hook-up wire used for interconnections. The Protoboard used for circuit assembly.. Neither the function generator, nor the oscilloscope is an ideal device. The function generator has output impedance and hence cannot deliver a voltage waveform to the circuit independent of frequency and test circuit configuration. The oscilloscope has input impedance that loads the circuit under test, inserting undesired impedance across the measurement points. We also need to consider the effects of the wiring used to connect the instruments to the circuit under test. Socalled 50 Ohm coaxial cable, for example, usually is used to connect the function generator to the circuit under test. At the frequencies at which most of our circuits operate, a short length of coaxial cable used for straight through connections will appear (usually) as a capacitor connected across the instrument terminals. This capacitor between the connection nodes will shunt the output of the circuit under test. ON the other hand, the relatively long pieces of hook-up wire used to connect the power supply to the circuit (usually) can be modeled adequately as inductance in series with the power source and the circuit. Finally, the Protoboards we use to support and interconnect our circuit components also introduce parasitic effects that influence the performance of our designs. These effects are most noticeable at higher frequencies. 2. Function generator. As noted in the support document, the function generator can be modeled as an ideal voltage source with a 50Ω series resistor as its output impedance. This model will be adequate for all experiments in this course. 3. Oscilloscope. The oscilloscope will normally connect to the circuit under test using 0x probes. To the circuit under test, the probe will look like a 5 pf capacitor in parallel with a 0 MΩ resistor connected between the measurement point and ground. The loop of wire formed by the probe tip and the ground connector will exhibit some inductance, but we will be able to ignore this inductance at the frequencies at which we will operate. At first glance, this looks like a large impedance, but a tabulation of the scope impedance with frequency reveals some interesting features. The probe looks like a pure capacitor at frequencies above about 6 khz. and its

2 2 capacitive reactance drops by an order of magnitude for each decade increase in operating frequency! Thus, at 5 MHz., the top frequency of our function generator, the scope probe looks like 000 Ω of capacitive reactance nowhere near 0 MΩ impedance! We will have to take this loading into account in later experiments. Frequency Frequency Input Input Impedance Rad/sec Hz reactance resistance magnitude E+.00E+07.00E E+0.00E+07.00E E+09.00E+07.00E+07, E+08.00E E+06 0,000.00, E+07.00E E+06 00, , E+06.00E E+05,000, , E+05.00E+07.00E+05 0,000,000.00,59, E+04.00E+07 Table. Oscilloscope probe impedance.00e+04 Aside: We frequently will find it useful to make the following approximation: A complex impedance (or admittance) function: Z R + jx Has magnitude: Z R 2 + X 2 If one term (R or X) is less than /0 the other, that term can be neglected with little error. Assume, for example that the reactance term (X) is /0 the size of the resistance one: X 0. R Then: Z R 2 + (0.R) R.00498R! R The effect is illustrated clearly in the impedance function for the scope probe. Here, the resistor and capacitor are in parallel, so admittances set the dominance of resistive or reactive results. Below about 000 radians/second the probe capacitive reactance is greater than 0 times 0 MΩ, so its admittance (/X) is less than /0 the conductance (/R) of the resistor, and the probe looks like a resistor. At 00,000 radians/second and up, the probe capacitive reactance is less than /0 its resistance. The probe effectively places a pure low reactance capacitor across the measurement points! 4. Protoboard parasitic capacitance. Our Protoboards are less than ideal interconnect systems. Their principal defect is the parasitic (undesired) capacitance that exists between adjacent rows of interconnection pins. The model for this parasitic capacitance is shown in Figs. and 2. We will use our scope probes (and the above impedance approximation) to measure

3 3 this parasitic capacitance and demonstrate how a simple circuit rearrangement called a Faraday shield can reduce this parasitic. Fig. Protoboard parasitic capacitance circuit model Function generator Scope probe Protoboard Scope probe Fig. 2. Protoboard parasitic capacitance measurement circuit It is always nice to get an estimate of what to expect when we conduct a physical experiment, so we will first use Multisim to simulate the circuit that we expect to see. A reasonable estimate of the inter-pin capacitance for the Protoboard is 0.5 pf, and 5 pins are wired together, so our circuit, including scope 0x probe input impedance looks like that in Fig.. The Bode plotter function (you may also use the oscilloscope instrument in Multisim) is used to track circuit response at frequencies below and above the point where the probe looks like a capacitor.

4 4 Using our 0 to impedance assumption, we can assume that the scope output probe impedance is pure capacitance at high frequencies and can infer the pin capacitance from the simple circuit equation: V o +!C probe!c probe! C probe + C probe + C probe Solving for the Protoboard capacitance: V o! V o C probe We measure the ratio of the two scope voltages to obtain V o / and insert the probe capacitance to obtain the board capacitance. To check our derivation, use the simulation results to see if we obtain the fictitious board capacitance used in the simulation.! 20log 0 # " V o $ & '6.90 (! V $ '6.90 o # & ' % " % Check! V o! V o C probe i pf.! Run the experiment in the lab using real measurements of the input and output voltages to estimate your real Protoboard capacitance. Use relatively high function generator output voltages to maximize the voltage at the scope probe connected to the open Protoboard pins. This will minimize the effect of extraneous noise on your measurements. You might want to use ONE LEAD of a resistor as a tie-point for your alligator clips. In other words, insert a resistor into each of the adjacent Protoboard row holes and clip each lead to the appropriate resistor wire next to the hole to complete your circuit. Obviously, any resistor value will work, since its other lead floats. Record input-output scope probe voltages in decade frequency steps (, 0, 00, etc., khz.) and fill in with some data points where the output voltage magnitude begins to change. Note how the input-output voltage ratio remains constant above a certain frequency, just as predicted by our capacitance approximation. Once you have calculated the measured capacitance, repeat the Multisim simulation with the capacitance you measured (divided by 5, of course, for each pin pair) inserted in the circuit. Note how well this simulation agrees with your measurements. To compare your results, you will have either to convert the scope input-output measurement ratio to db., or convert the Bode plotter output to voltage ratio.

5 5 5. Faraday shield. One way to reduce the effect of this capacitance on our circuit performance and it will have a significant effect on circuit performance in our very first transistor amplifier experiment is to avoid using adjacent rows on the board and ground the intermediate row of pins. This insertion of a ground plane between conductors is called a Faraday Shield. The model for the new parasitic condition due to the Faraday shield is shown in Fig. 3. Its effect is illustrated and simulated in Fig. 4. In an ideal shield, both sets of parasitic capacitors are connected to ground and therefore there is no coupling from the signal source to the output measurement point. The 0.25 pf capacitor inserted in our simulation model is intended to show that the shielding is imperfect some signal will leak through and around the shield. Fig. 3 Protoboard Faraday shield parasitic capacitance circuit model - ground intermediate row of pins For this lab, repeat the previous experiment on a real Faraday shielded Protoboard, to estimate the shield leakage capacitance. As before, check your results by replacing the estimated 0.25 pf capacitance with your measured leakage value and re-running the simulation. Fig. 4. Faraday shield parasitic capacitance measurement circuit ground intermediate row of pins 6. Coaxial cable. A short length of coaxial cable open at one end will appear as a capacitor (two conductors separated by an insulator) to connections at the other end, while the same short section, when short-circuited at the far end will

6 act as an inductor (a loop of current-carrying wire). 6 This interpretation can be extended: If an imperfect open circuit a high impedance - is connected to the far end of the coax, the coax will still behave like a capacitor at its input terminals and if an imperfect short - a low impedance - is connected, the coax will still look like an inductor at its input terminals. Since we generally will not terminate coax in a low impedance, this experiment will study only open-circuited coax characteristics. To conduct the experiment, select a meter length of coax with a BNC connector on one side and alligator clips on the other. One alligator clip will connect one side of the coax to the function generator. The other will connect to the scope through a 0x probe. (If you wish, you may run this experiment with a 2 meter length. Just use a BNC coupler to connect two of our lab coax sections at their BNC ports.) For the simulation, you will need to convert your length of coax to parameters that Multisim understands. In addition to the characteristic impedance of the line, one must use one of two ways to describe the coax length of coax: 6.. Either the time delay that a wave experiences passing through the line (e.g. e-09 seconds), or 6..2 The length of the line in wavelengths at a given frequency (e.g. /4 wave at 3e6 Hz). If we choose the second approach, we take the following actions to replicate a meter line: 6..3 Note that the speed of light in free space is 3*0^8 meters/second The free-space wavelength,, of a 30 khz signal is 0,000 meters, since the distance traveled by a wave in space in the time of one cycle is:! 30i0 3 3i08 0,000 meters A meter line definitely is a short transmission line at 30 khz! Wave propagation through transmission lines with dielectric material other than air, however, is slower than through free space. We shall not attempt to derive any electromagnetic filed expressions here. Instead, we simply note following specifications (Belden 829) for RG-58A/U coax of the type used in our lab: Nominal characteristic impedance - Ω Nominal Inductance µh per foot Nominal capacitance pf per foot Nominal relative velocity of propagation (%) Nominal delay nanoseconds per foot Nominal inner conductor resistance ohms per 000 feet - Ω Nominal outer conductor resistance ohms per 000 feet - Ω Comments 53.5 About sqrt(l/c) µh for meter pf. for meter 73 Equivalent to km/second nanoseconds for meter 8.8 About 0.03 Ω for meter 4. About 0.05 Ω for meter Table 2. RG-58A/U specifications Since a meter length of RG-58A/U is 0.000/ wavelength at 30 khz, the entry data for RG- 58A/U is:

7 7 Nominal impedance (Zo) 53.5 Ω Frequency (F) 30e3 Hz Normalized electrical length (NL) wavelength Double the electrical length if you use 2 meters of coax. 6. Open length of coax A short piece of coax should act as a capacitor. The following simulation demonstrates this capability for a 2 meter length of RG-58A/U cable of the type used in out lab. You can use the previous Protoboard setup to wire this circuit, simply clip each lead of the coax to one of the resistor tie points. The Protoboard capacitance and the coax capacitance are now in parallel and you will measure their sum. Fig. 5. Open-circuited 2 meter length of RG-58A/U Record the input and output scope voltages at decade frequencies (khz, 0 khz., etc.) and again, fill in with several data points where the output voltage changes. Just remember that the RATIO of output to input voltage is the quantity of importance. To estimate the coax capacitance, use the derivation and formula from the Protoboard section of the lab. Given your estimate, run a Multisim simulation using your measured value and compare the Multisim frequency response with your experimental results.

8 7. Report requirements. In your report present and discuss your Multisim simulations, measured results and estimated parasitic capacitances for all the parasitic conditions addressed in the experiment. Discuss the degree of agreement between simulation/theory and measurement, and what may be cause for any significant deviations. 8 Prepared by Philip V. Lopresti (updated by KRL 27 August 2007)