Experiment 1: Instrument Familiarization (8/28/06)

Electrical Measurement Issues Experiment 1: Instrument Familiarization (8/28/06) Electrical measurements are only as meaningful as the quality of the measurement techniques and the instrumentation applied to the measurement. It is easy to use modern instruments to get a reading, such as voltage with a DMM. In many situations that reading may not represent what you really wanted, however. This experiment explores a few of the more common ways in which defects in measurement technique can corrupt the measurements taken. Instrument Loading Whenever a measurement instrument is connected to a circuit, it will alter the operation of that circuit because it will draw some power from the circuit. A well-designed measurement will minimize this disturbance, or at least correct the reading for it. It is easy to forget to consider this effect, however, and get a reading that is completely misleading. Most measurement situations can be modeled by a Thévenin Equivalent source representing the circuit you are measuring, and some impedance placed across that source, representing the measurement instrument. Z s V s Z i Here V s is the source voltage, Z s is the source impedance and Z i is the instrument impedance. The goal is to measure V s, but what we actually measure with our instrument is the voltage across Z i, i.e., [Z i /(Z s +Z i )] V s. Clearly we want Z i to be as large as possible relative to Z s. Let s look at an example. Consider a measurement: V s 10K 10 M 15 pf Here Z i has been replaced by the equivalent circuit of an oscilloscope using a 10x probe. These component values are typical of 10x scope probes, and a measurement situation on a typical low frequency transistor circuit. Clearly, at low frequencies, the 10M probe resistance will cause little voltage drop across the 10K resistor. The 15 pf capacitor will cause a voltage drop at very high frequencies. It is very straightforward to calculate the voltage across the probe versus frequency, shown in Figure 1. - 1 -

1 Attenuation vs. Frequency Attenuation, Vout/Vin 0.1 0.01 1 10 4 1 10 5 1 10 6 1 10 7 1 10 8 Fig. 1: Frequency, Hz Notice that although 10x probes such as this are specified as being usable up to 200 MHz, the high impedance of the source is resulting in a 3 db loss at only 1.0 MHz! The higher the frequency and/or the higher the source impedance, the more critical it is to analyze your instrumentation to make sure you can make an accurate measurement. Consider a typical radio frequency (RF) measurement with a 50 ohm source impedance. The attenuation curve is now that shown in Fig. 2: 1 Attenuation vs. Frequency Attenuation, Vout/Vin 0.1 1 10 4 1 10 5 1 10 6 1 10 7 1 10 8 Fig. 2: Frequency, Hz Now, because of the much lower source impedance, the measurement is good to a much higher frequency. Note, however, that the measurement is down by over 3 db by 100 MHz. Clearly measurements at high RF frequencies are problematical, even with a 10 Mohm scope probe. Most Digital Multimeters (DMMs) have very high input resistances as voltmeters, often in the 10s of Megohms, and rarely load DC circuits. In high frequency circuits, however, the DMM probes and wires can easily act as antennas and pick up or radiate RF energy to and from different parts of the circuit. In circuits such as oscillators, the test leads can easily prevent oscillation or, in amplifiers, induce oscillation. Such changes in circuit operation often change the circuit bias points and thus the DC voltages present. The result is, again, that the measured DC voltage is not representative of the voltage present in the undisturbed circuit. - 2 -

Many RF instruments, such as spectrum analyzers and network analyzers, have 50 ohm transmission line inputs. Some oscilloscopes can be set to 50 ohm input impedance (vs. the 1Meg typical). This is very convenient at RF frequencies since connections between unmatched transmission lines produce reflections. These reflections not only reduce the signal reaching the measurement circuits, but they also return RF energy back to the circuit at a different phase, with unpredictable (usually undesirable) impact on the circuit performance. This relatively low impedance is a problem, however, if the circuit source impedance is not 50 ohms. For RF and high speed pulse circuits, matching the impedance of the circuit to the measurement instrument is critical to getting a meaningful measurement. Parasitic components Even in low frequency measurements, unintended circuit elements can creep into the measurement circuit without your being aware of them. Consider, for example, the measurement of a small resistance, say 1 ohm. If you use a standard handheld or bench DMM, you would connect test leads between the instrument and the resistor. A six-foot test lead can have a resistance of 0.08 ohms just in the wire. Contact resistance can easily add another 0.1 ohm, resulting in 0.18 ohms in excess of the 1.0 ohm resistance being measured. This is a 18% error. A more common problem is the ground lead of oscilloscope probes. The ideal measurement with a scope probe has the ground ring at the tip of the probe grounded to the circuit ground right next to the circuit node being measured. More often, we make do with the short ground lead clipped to some convenient ground point within 6 inches or so. This works fine for low frequency signals below about 10 MHz. At much higher frequencies, the impedance of the shunt capacitance in the probe becomes comparable to the impedance of the ground lead inductance. The plot below shows the impedances of a 15 pf capacitor (representing the probe shunt capacitance) and a 1 µh inductor (representing the probe ground lead about 3 inches long). 1 10 5 Fig. 3: Impedance vs. Frequency 1 10 4 Impedance, ohms 1 10 3 100 10 1 1 10 6 1 10 7 1 10 8 1 10 9 1 10 10 Frequency Z(1uH) Z(15pF) - 3 -

Where these two curves cross (Figure 3), the inductive and capacitive reactance are equal. This is a resonance condition and can result in amplification of the signal observed. Above this frequency the observed signal will be attenuated at about 40 db per decade of frequency. These effects often explain the ringing waveforms seen following a fast voltage step on an oscilloscope. Whenever you see these, you should ask yourself if they are really there, or if it is an artifact of improper grounding. Sometimes people will try to make single wire measurements with only the tip of the scope probe connected to their circuit. You must understand that a single wire measurement is fundamentally impossible; voltage has meaning only with reference to some assumed ground, and currents are only conducted around closed loops. What is really happening is that the signal currents are returning to the circuit under test via the scope ground wire in the power cord and other wires connected to the circuit. In some cases, stray capacitances provide the return current path. In any case, the associated inductance in this ground return can be huge and impact the waveforms observed even at very modest frequencies. Instrument accuracy In general, the more specialized the instrument, the more accurate it will be for that measurement. DMMs can measure voltages more accurately than an oscilloscope. An oscilloscope is much more suitable for observing how voltages change in time. Oscilloscopes can be used to measure frequencies, but a frequency counter is far more accurate. When more than one frequency signal is present at a time, a spectrum analyzer is often more useful for separately measuring their separate amplitudes. The terms Accuracy, Sensitivity, Resolution and Precision require some discussion. Consider a measurement of a voltage with a DMM. The display reads 1.039 volts. Suppose that we knew by some other means that the true voltage was 1.037271654859 volts exactly. The difference between the true voltage and the displayed voltage is the error in the measurement. This error may be due either to an error in measurement technique (e.g., lead resistance, thermocouple voltages, noise, circuit loading, etc.), a calibration error, or to a limitation in instrument sensitivity or resolution. Accuracy is the term we use when we try to characterize how well the instrument is calibrated. Accuracy is a measure of how closely the displayed readings would match the true values. Sensitivity is the smallest change in the input signal that can be detected by the instrument. Resolution is a measure of how small a change in signal will result in a reliable change in display value. Sensitivity needs always to be better than display resolution so that resolution is the limiting factor. Consider a frequency measurement with a poorly calibrated frequency counter. The counter displays 10 digits. If the source frequency is stable enough all 10 digits may be stable. A small change in the source frequency by one part in 10 10 may be easily detectable and is displayable. Such a measurement would have a resolution of 1 part in 10 10. If the counter time base was off by 10%, however, the accuracy of the measurement would only be 1 part in 10, or 10%. Never the less, such an instrument could be quite useful for a measurement comparing two frequencies that were quite close to each other, provided one of the frequencies was known accurately. - 4 -

Also consider a similar measurement of the frequency of an unstable oscillator using a well calibrated counter. Perhaps only the first four digits of the display are giving consistent readings and the rest are constantly changing. The instrument is accurate. The instrument and the measurement have a high resolution. Never the less the measurement is not very precise. Part of the accuracy of an instrument is how stable it is over time and temperature. Clearly an instrument that meets its claimed accuracy within a few minutes of being turned on, and shows negligible drift over temperature and time, is much more useful than one that drifts for hours or days after being turned on, or whose calibration changes significantly for even small changes in room temperature. While for most routine measurements our modern instruments are more than accurate enough, sometimes we require an exceptionally accurate measurement. In those cases we need to research carefully the performance of the instruments used, and carefully design the measurement so that we don t introduce errors. Impedance Matching When designing an experiment, it is important to remember that every source has an output impedance. Likewise, every load has an input impedance. As you studied in your Intro to Electrical Networks course, maximum power transfer occurs when these impedances match. For a simple resistive circuit, this means that the load resistance should equal the source resistance. For a circuit with a complex source impedance, the load impedance should equal the complex conjugate of the source impedance. In addition to maximum power transfer, matched impedances also determine the amount of signal reflected at an interface. For example, reflections along transmission lines can cause the voltage source to see reflections with a different phase than the source signal. This can become a significant problem when cable lengths reach several hundred feet in length. The function generators in the lab can be set to accommodate an output termination (load impedance) of either 50Ω or an open circuit (High Z). Note that the termination setting has the effect of changing the voltage displayed by a factor on 2 to account for the load impedance. It is important to always note and record the output termination (50Ω or High Z) for which your function generator is set. You should also think about which output termination is appropriate for the device you are testing. Be careful, the output termination setting can change when you turn the function generator off and on and the output voltage will change when you toggle the termination impedance. True RMS The rms value of a periodic voltage is often considered to be V peak / 2. However, this is only true of sinusoidal signals and does not hold for most mixed analog signals. The textbook definition of a root mean square (rms) voltage is: (1) - 5 -

It is important to remember this definition when you are making a measurement. It is of equal importance to know how each measurement device defines a rms measurement. To understand the reading that a measurement instrument displays, either refer to the manual or conduct your own experiment using signals whose rms values are easy to predict. An important property of a rms value is that, over a given time period, the energy delivered to a load from a rms source will be the same as the energy delivered to the same load from a dc source of the same value. This makes the rms value useful in power calculations and is often the way we speak about voltages (for example, line voltage is 120 Vrms). Experiment This experiment is designed to demonstrate some of the limitations of the instruments used in this lab and the worth of some proper measurement techniques. Along the way, we will see if we can verify that the HP 33120A Function Generator meets its specifications for a square wave. 1) Oscilloscope Rise Time Measurements: Measure the rise time of the square wave signal from the HP 33120A Function Generator using various, mostly improper, connections between the instruments: a) Set the function generator for a 1.000 MHz square wave. Be sure the output termination (under system ) is set to High Z and set the amplitude to1v p-p. Connect the Output Terminal (lower BNC jack on function generator) to the Analog Input 1 (A1) on the oscilloscope using 2 BNC to Banana Plug adapters and two 3 foot Banana plug wires. - Measure the rise time and overshoot of the rising edge of the square wave signal b) Repeat the same measurement, but this time connect the Output Terminal to the A1 scope input using a BNC cable. Do not terminate the cable (i.e., put on an impedance matching resistor) yet! - Measure the rise time and overshoot of the rising edge of the square wave c) Repeat the same measurement, but this time with a 50 Ω termination on the BNC cable at the A1 input to the scope. (Use a BNC tee). - Measure the rise time and overshoot of the rising edge of the square wave d) Repeat the same measurement, but this time set the function generator output termination (under system ) to 50Ω. - Measure the rise time and overshoot of the rising edge of the square wave - 6 -

e) Reset the function generator termination to High Z. Remove the BNC cable and connect the 10x probe to the A1 input on the HP54622D scope. Remove the probe hook adapter (if it is installed) and place the center pin of the probe into the function generator Output Terminal BNC, making contact with the BNC center conductor. Do not connect the probe ground to anything for this measurement! - Measure the rise time and overshoot of the rising edge of the square wave on the oscilloscope Record the waveform and any observations about it. - What is the signal current return path for this measurement? f) Repeat the last measurement, but with the probe ground wire clipped onto the shell of the Sync BNC on the function generator. - Measure the rise time and overshoot of the rising edge of the square wave signal g) Repeat the last measurement, but with the probe ground wire clipped onto the shell of the function generator Output Terminal BNC. - Measure the rise time and overshoot of the rising edge of the square wave h) Finally, repeat the last measurement, but use the probe-tip-to-bnc adapter, which grounds the probe ground ring directly to the BNC shell. - Measure the rise time and overshoot of the rising edge of the square wave signal i) Examine the HP33120A Function Generator and HP54622D Oscilloscope specification sheets and answer the following questions in your report: - What is the function generator square wave rise time specification? - What is the scope rise time specification? - What is the scope sample rate at the time scale you used? - How many samples did the scope make during the rise time? - Is the trace on the scope believable? Why? - Which of these measurements provides the most accurate measurement of the actual function generator square wave? What is your estimate for the uncertainty of your measurement; that is, how much faster could the rise time actually be, and how much slower, and still be consistent with your observations and the instrument specifications? - For each of the other measurements, why is it less accurate? - 7 -

2) Frequency Measurements: Measure the frequency of the HP 33120A Function Generator Output using the Oscilloscope and the HP 5384A Frequency Counter: a) Set the function generator for a 1.000000 MHz sine wave. Connect the Output (lower BNC jack on function generator) to the oscilloscope A1 input using a BNC cable. Use a 50 Ω termination on the BNC cable at the A1 input to the scope. By accessing the function generator menu commands, set the function generator output termination (under system ) to 50 ohm. Set the amplitude to 0.1 V pp. - What frequency do you measure on the oscilloscope? - How stable does the frequency appear? What uncertainty do you estimate for this measurement? - Vary the vertical and horizontal scales. Which settings appear to give the most reliable measurement? Why? b) Disconnect the BNC cable from the oscilloscope and connect it to the A input on the frequency counter, keeping the 50 ohm termination on the cable. - What frequency do you measure on the frequency counter? - How stable does the frequency appear? What uncertainty do you estimate for this measurement? - How closely does this frequency match the function generator set frequency? c) Reduce the function generator amplitude to give a 10 mv pp output (you may have to rig up an attenuator to do this). - Can you still measure the frequency on the frequency counter? - Can you still measure the frequency on the oscilloscope? - What is the smallest amplitude that each instrument can work with? d) Answer the following additional questions in your report, based on the instrument specifications: - What is the resolution of the oscilloscope for frequency measurements? - How accurate is the oscilloscope time base? - What is the resolution of the frequency counter for frequency measurements? - What is the accuracy of the frequency counter? 3) AC Voltage Measurements using the HP 3478A Multimeter: Measure the amplitude of the HP 33120 Function Generator Output using the HP 54622A Oscilloscope and the HP 3478A Multimeter: a) Set the function generator to output a 20 khz sine wave with an amplitude of 0.1 V rms. Make sure the output impedance is set to High Z. Connect the Output of the function generator to the A1 input on the oscilloscope using the BNC cable, but without the 50 ohm termination. - 8 -

- What V rms amplitude do you measure from the oscilloscope? - Does it agree with the function generator amplitude setting? If not, why not? b) Disconnect the BNC cable from the scope A1 input and connect it to the DMM, using a BNC to Banana adapter. - What V rms amplitude do you measure from the DMM? c) Set the function generator frequency to 1 MHz. - What V rms amplitude does the DMM give now? - Find the 3 db frequency for the DMM (where the reading is 0.707*V rms ). c) From the instrument specifications, answer the following questions in your report? - What is the smallest AC signal that the DMM can measure? - What is the smallest AC signal that the oscilloscope can measure? - What are the largest AC signals that each instrument can measure safely? 4) AC Voltage Measurements using the Protek B-845 Multimeter: Measure the amplitude of the HP 33120 Function Generator Output using the HP 54622A Oscilloscope and the Protek B-845 Multimeter: a) Set the function generator to output a 20 khz sine wave with an amplitude of 0.1 V rms. Make sure the output impedance is set to High Z. Connect the Output of the function generator to the A1 input on the oscilloscope using the BNC cable, but without the 50 ohm termination. - What V rms amplitude do you measure from the oscilloscope? - Does it agree with the function generator amplitude setting? If not, why not? b) Disconnect the BNC cable from the scope A1 input and connect it to the DMM, using a BNC to Banana adapter. - What V rms amplitude do you measure from the DMM? c) Set the function generator frequency to 1 MHz. - What V rms amplitude does the DMM give now? - Find the 3 db frequency for the DMM (where the reading is 0.707*V rms ). c) From the instrument specifications, answer the following questions in your report? - What is the smallest AC signal that the DMM can measure? - 9 -

- What is the smallest AC signal that the oscilloscope can measure? - What are the largest AC signals that each instrument can measure safely? 5) AC Voltage Measurements with 60 Hz sinusoidal interference: Measure the amplitude of a low level square wave signal in the presence of 60 Hz sinusoidal noise with an amplitude greater than the signal: a) Set the HP 33120A Function Generator to output a 20 khz square wave with an amplitude of 0.1 V pp. Set the HP3312A Function Generator to output a 60 Hz sine wave with about 0.2 V pp amplitude. Improvise two 1 kω resistors to mix the two signals together. Using an unterminated BNC cable, attempt to observe the 20 khz component of the combined signal on the oscilloscope. - Can you synchronize the scope on the desired 20 khz signal using internal triggering? - Can you estimate the amplitude of the 20 khz pulses? How accurate do you think this measurement is? b) Disconnect the BNC cable from the scope and connect it to the DMM. Does this measurement help you at all to measure the 20 khz square wave signal? Why not? c) Reconnect the BNC cable to the scope. Connect another BNC cable from the HP33120A function generator Sync output to the oscilloscope external trigger. Set up the scope to trigger on the Sync signal and observe the A1 trace. Can you now measure the 20 khz square wave signal amplitude? d) Set the oscilloscope to display an average of 256 traces. Now can you see the 20 khz square wave signal? How well can its amplitude be measured now? Record your best estimate of the amplitude, and how much uncertainty you have in this value. Report 1) Oscilloscope Rise Time Measurements: Prepare a table listing all the measured rise times and overshoot values measured. Discuss your conclusions from this exercise. Answer all the questions, briefly. 2) Frequency Measurements: List all the frequency measurements, and how much uncertainty (be quantitative) you estimate for each. Answer all questions, briefly. 3) AC Voltage Measurements using the HP 3478A Multimeter: Answer all questions briefly. 4) AC Voltage Measurements using the Protek B-845 Multimeter: Answer all questions briefly. 5) AC Voltage Measurements with interference: Record the answers to all questions, and the final measured value and estimated uncertainty. - 10 -