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The oscilloscope is a wonderful measurement tool but if it is not used carefully it can give highly misleading results. You can achieve the full potential of your scope but only if you know what you are doing. This article gives some good tips on oscilloscope use. By BRYAN MAHER Say you have invested hard cash in a good quality oscillo­scope. It looks a beautiful instrument and the specs guarantee it to be accurate within 2%. Wow! And its bandwidth is wide enough to make your friends drool. But a scope is only a tool, no matter how glossy the liter­ature. If you don’t use it properly you will be disappointed with the results. Let’s start with a simple DC measurement, using the circuit shown in Fig.1(a). If we read the DC voltage at point D, a digital voltmeter (DVM) gives a reading of +4.9V. If we then connect the oscilloscope via a 1x shielded probe, the deflection on the screen is likely to indicate only about +4.17V. Which is correct? Clearly that 64  Silicon Chip scope probe is loading the source of this measurement, pulling the voltage down! “Source” here means any part of circuit at which we make a measurement. In this case it is point D in Fig.1. And “source resistance” or “output resistance”, denoted by Rs, means the ratio of the change in voltage at that point (caused by attaching the probe) divided by the minute current drawn by the probe. This is denoted by the expression: Rs = (∆v/∆i) Ω. Because it is a voltage/current ratio, we call it resist­ance (ohms), even though it is a calculated quantity. Only rarely is Rs a single physical component. Nevertheless Rs does have the ability to upset the workings of a circuit. “Delta” simply means a small change in any quantity. Equivalent circuit The equivalent circuit, illustrated in Fig.1(b), reveals how this loading effect occurs. The input resistance of the direct 1x probe connection is just the 1MΩ resistor within the scope, which we have called R1 in Fig.1(a). R1 and Rs actually form a voltage divider, so the scope sees only the voltage at D, which is the true voltage of the source reduced by the fraction (R1/(R1 + Rs)). Typically, a digital multimeter has an input resistance of 10MΩ so using it has a less deleterious effect on the voltage. This is why the DMM reading is higher, at +4.9V. You can calculate the value of the source resistance Rs in this case from these measurements and the definition given above. It works out to be about 200kΩ which is reasonable for this particular op amp circuit. Let’s define V as the unloaded output voltage of the source; ie, the potential at point D when neither the scope probe nor the DMM is connected to it. Using the voltage divider equa­ tion, the voltage Vpat D when only the 1x probe and scope is hooked on is: Vp = V(R1/R1 + Rs) = V(1MΩ/1.2MΩ) = V/1.2 The scope reads Vp as +4.17V, so the unloaded output vol­ tage at the point D is: V = (1.2)(4.17) = 5V The relatively low resistance of the scope input was the cause of the loading effect. It loaded the source and so caused the oscilloscope to read +4.17V instead of the true +5V. Measurement rule-of-thumb The cure for this loading effect is now obvious. The test instrument should have an input resistance much greater (prefer­ably 100 times greater) than the output impedance of the source to be measured. A 100 times factor would limit loading errors to about 1%. But practical aspects like price, availability and frequency response will limit our selection of scope probes. A common favourite, the 10x probe, as illustrated in Fig.2, is an excellent choice in most cases. This type of probe contains a 9MΩ resistor called Rp. Therefore the total probe connection resistance, Rin, is equal to Rp in series with the scope input resistance, R1. That is: Rin = (Rp + R1) = (9MΩ + 1MΩ) = 10MΩ If we substitute this 10x probe in the measurement shown in Fig.1, the oscilloscope would display a deflection of +4.9V, the same as the DMM reading, a satisfying result. Fig.1: this dual phase amplifier (a) has a 5V output at point D where the source resistance is 200kΩ. But clipping the 1MΩ probe onto this point pulls the voltage down to 4.17V. The equivalent circuit (b) shows that the source resistance Rs forms an unwant­ed voltage divider with R1, the input resistance of the 1x probe and the scope. This reduces the voltage seen by the scope. High voltage measurements Fig.2 shows a second important use of the 10x probe. Here the source resistance is quite low (due to negative feedback) at the collector of transistor Q1 so loading is not a worry but the high voltages are! In this case we can use the fact that Rp (in the probe head) and R1 (in the oscilloscope) form a deliberate voltage divider. Any voltage which we apply to the probe tip will be reduced at the scope input terminal. The reduction fraction is: Vsc = R1/(Rp + R1) = 1MΩ/(9MΩ + 1MΩ) = 1/10. That’s why this probe is known as a 10x, because it produc­es a 10:1 voltage attenuation. In the circuit of Fig.2, the high volt- Fig.2: the 9MΩ probe resistor Rp and the 1MΩ scope input resistor R1, form a deliberate voltage divider. This reduces the voltage at the oscilloscope input terminal to one tenth of that at the probe tip. age of the supply (+450V) rules out use of the 1x probe and forbids direct connec­tion to the scope’s input. But the 10x probe is suitable, provid­ed it has a voltage rating above 450V. This probe will reduce all waveform voltages to one tenth and the DC voltage at the scope input will be no more than +45V. By dividing down the signal, the 10x probe effectively multiplies the V/div calibration on the attenuator switch by a factor of 10. So a 5V/div setting now means 50V/div and eight vertical divisions on the screen will correspond to a 400V range. Hence this 360V signal fits within the graticule limits. Many top line scopes can sense when the 10x probe is con­nected to the modified BNC input terminals. Then internal logic circuits multiply the August 1996  65 Fig.3: source (a) has output resistance Rs equal to 50Ω at point D. The high frequency equivalent circuit (b) shows that Cp forms an unwanted voltage divider with Rs. Cx represents the combined stray capacitance of the coaxial cable and the scope input. 10x probe) we must be aware that the probe tip still carries a lethal 360V! For safety we must keep the amplifier 0V line connected to the scope frame and to mains earth. And we never unplug the probe from the scope while the probe tip is still hooked onto a high voltage point. All probes which contain only resistors and capacitors are called passive and oscilloscope manufacturers market a range of higher resistance units. A few of these are listed in Table 1 but not all probes on the market have voltage ratings as high as those shown here. Direct 1x scope probes have only a small series resistance so they cause little attenuation of the signal being measured. They are useful for the display of very small voltages of low frequency signals, when measured at low impedance points, such as the outputs of op amps. Some less common sources, like biological assay electrodes, have an extremely high output resistance. To display signals from these, active probes are required. Typically, these employ IGFETs and other active circuitry to provide an input impedance of 10GΩ and zero input capacitance. Oscilloscope bandwidth Fig.4: the amplitude response of an oscilloscope falls at high frequencies. At full rated bandwidth, the response is -3dB or 30% lower than it is at low frequencies. on-screen readout by 10, to correctly display the voltage value at the probe tip. This facility is not provided in cheaper scopes and nor does it work when a scope is used with a probe of a different brand. Safety precaution Though the oscilloscope is safely working on reduced input voltages (because of the attenuation by the Fig.5: With AC (capacitive) coupling, the signal passes through a high pass filter. This will reduce the amplitude of low frequency signals and distort low frequency pulse waveforms. Table 1 Probe Attenuation 1x 10x 100x 1000x R(in) 1M 10M 10M 100M 66  Silicon Chip Maximum DC Voltage 350V 600V 1.5kV 20kV Derated Above Derated to 1MHz 200kHz 100kHz 30V <at> 20MHz 300V <at> 20MHz 2kV <at> 20MHz Another scope parameter which new users often have diffi­culty coming to terms with is bandwidth. This could be easily measured if you had a synthesised RF signal generator with an output of 5V over a frequency range from 100kHz to 250MHz and an output impedance of just 50Ω. You might think that such a wide­ band source could easily demonstrate a scope’s bandwidth. Would you just connect the 10x probe to the generator and then sweep over the frequency range? Fig.3 illustrates the setup, with the probe’s internal resistance and capacitance shown. However, you might be disappointed to find that, when the gen­erator was set to the advertised bandwidth frequency of your high performance scope, say 250MHz, the vertical deflection is only half what it should be. So what does scope bandwidth mean? The bandwidth of any oscilloscope is that high frequency at which the response has fallen to 70.7% (-3dB), compared to the reference frequency value, as illustrated in Fig.4. This Table 2 Taken from a Tektronix TDS360 digital oscillo­scope, this screen printout shows the effects of incorrect ad­justment of 10x probes on the scope’s internal 1kHz compensation signal. Channel 1, the upper trace, shows too much probe ca­pacitance (over-compensation) while the channel 2, lower trace, shows insufficient capacitance (under-compensation). The correct probe compensation adjustment would show a square wave with “square” corners. This scope printout shows the effects of DC and AC cou­pling on a pulse waveform with uneven duty cycle. Channel 1, top trace, is DC coupled and it can be seen that the voltage swings equally above and below the zero reference line (solid horizontal cursor). Channel 2, lower trace, is AC coupled and the waveform has floated down with respect to the zero reference line (dotted horizontal cursor). shows that the response of any oscilloscope is down by 30% at its advertised full bandwidth! Furthermore, Fig.4 shows that the manufacturer’s guarantee of an amplitude error of less than 2% only applies for signal frequen­cies less than one quarter of the rated bandwidth. Frequency Capacitive Resistance 1MHz 10MHz 50MHz 100MHz 250MHz 300MHz 400MHz 13.3k 1.3k 265 132 53 44 33 Therefore, to make amplitude measurements with less than 2% error, we need a scope with a quoted bandwidth four or five times higher than the signal frequency. For example, accurate amplitude display of a 50MHz sinewave requires a 250MHz oscilloscope. This is only part of the bandwidth story. As we noted above, testing an oscilloscope with a wideband generator could show an error of more than 50% at the advertised scope bandwidth. How could it get worse? In most cases the advertised -3dB bandwidth of a scope applies only when signals are coupled directly into the instru­ment front terminal and not via a probe, because probes also have frequency limitations. This is demonstrated by Fig.3(b), which is the high fre­quency equivalent of the circuit shown in Fig.3(a). As before, the resistance presented by the probe and scope connection is: Rin = (Rp + R1) = 10MΩ where Rp is the resistance inside the probe and R1 is the input resistance of the oscilloscope. In the equivalent circuit of Fig.3(b) we can ignore the 10MΩ input resistance Rin because it is so much higher than the 50Ω source resistance Rs. But we cannot discount the probe’s input capacitance Cp which is equal to 12pF. The capacitive reactance of Cp is: Xc = 1/(2πfCp). This forms an unwanted voltage divider with the source resistance Rs. At high frequencies the resulting low value of Xc drastically reduces the signal amplitude before it enters the scope. Table 2 demonstrates the severity of this effect, with the reactance of 12pF at specific frequencies. From Table 2, we observe that at 250MHz the probe’s capaci­tive reactance has fallen to 53Ω. Now we will August 1996  67 Fig.6: since a PWM signal has a varying duty cycle and therefore an effectively varying positive and negative DC offset, AC cou­pling will cause the waveform to waver above and below the 0V reference line. see the reason why the amplitude displayed on the screen fell to 50%. Firstly, looking at Fig.4(b), we see that at 250MHz the voltage divider effect of the 53Ω Xc with the 50Ω source resistance Rs reduces the signal voltage at D down to 70% of the unloaded source voltage (it’s a vector calculation, because of the ca­pacitor). Secondly, as Fig.4 shows, the displayed amplitude will be further reduced to 70% of the voltage at the scope input, because the signal frequency is now equal to the 250MHz bandwidth of the scope. So the amplitude you would see on the screen will be reduced to (70% x 70%) = 50% of the unloaded source voltage. That explains why a high frequency measurement with a 10x probe can have such large errors. Table 3 Attenuation R(in) C(in) 1x 10x 10x 100x 10x 10x 1M passive 10M passive 10M passive 10M passive 100k active 500 divider 55pF 12pF 8pF 2.7pF 0.4pF 0.15pF 68  Silicon Chip Only in a few cases will a manufacturer guarantee that the advertised bandwidth applies at a specified probe tip. Examples include the Tektronix 400MHz oscilloscope model 2465B but only when used with their 1MΩ passive 10x probe model P6137. Table 3 shows the input capacitance and bandwidth of typi­cal probes. Frequency pulling Often, the application of a passive scope probe to some points of a circuit can have drastic effects, particularly in the case of crystal and other oscillators. These require critical positive feedback gain and phase, set by specif­ic small capacitor values, to maintain oscillation at the re­quired frequency. But hooking a passive probe onto a high im­pedance point of these circuits can add 12pF of capacitance, upsetting the feedback. This action can either reduce the Bandwidth operat­ing frequency or may stop oscilla15MHz tion altogether. 100MHz How do we avoid 500MHz this? Many systems, 250MHz including some TV 4GHz re­c eivers, contain buffered test points, 9GHz where sensitive circuits are access­ed either via an inbuilt resistor or a low impedance source follower. Alternatively, a simple expedient is to attach a small resistor, about 10kΩ, to the probe and use the other end of that resistor as the probe point. The results may be inaccurate but at least you can monitor the waveforms. Another alternative is to use a high impedance active probe, such as listed in Table 3. For frequencies above 500MHz, wideband active FET probes are available with a high input impedance and they require a separate supply. Examples include the Tektronix type P6204 which has a 1GHz bandwidth and the type P6217 which operates to 4GHz. Active probes accept small input voltages, typically below 10V. For really wide bandwidth scopes, between 2GHz and 10GHz, low impedance divider probes are available, with input resistanc­es of 50Ω, 500Ω or 5kΩ. They plug into the 50Ω input terminals on very high frequency oscilloscopes. Probe risetimes Another area where a new oscilloscope can disappoint is when displaying square waves which are supposed to have fast rise and fall times. Fig.3(a) shows the connection as before and now we will explain why the probe capacitor Cp is there at all, in view of the trouble it causes when displaying very high frequen­cies. The reason why Cp is inside the and undershoot. Naturally this Cp adjustment also has a big effect on the displayed bandwidth so if you don’t adjust it correctly, it is yet another source of measurement error. AC coupling This scope printout shows the effects of DC and AC cou­pling on a pulse waveform with varying pulse width (ie, pulse width modulation). Channel 1, top trace, is DC coupled while Channel 2, the lower trace, is AC coupled. The varying pulse width effectively becomes a varying DC offset which is reflected as a wavy modulation on the waveform, an erroneous display. This is the same effect as depicted in Fig.6. probe becomes clear when you look at pulse risetimes. The probe’s shielded cable and the oscilloscope’s input stage add up to a considerable capacitance to ground, probably between 35pF and 100pF. This we denote as Cx in Fig.3(a). If Cp did not exist in the probe head, then the probe resistor Rp, together with this stray capacitance Cx, would form a severe low pass filter. The effect would be a reduction in amplitude and a phase change in sinewave signals and a drastic slowing of the risetime of pulses as displayed on the screen. Therefore the capacitor Cp has been deliberately included in the probe to correct these errors. But Cp must be correctly adjusted until the two time constants, RpCp and R1Cx, are equal. To facilitate this adjustment, most oscilloscopes provide a fast-risetime 1kHz square wave calibrating signal from a terminal (usually) on the front panel. You just hook the probe onto this CAL terminal and adjust the probe capacitor Cp until the scope displays a true square wave. If Cp is set too low, the square wave will be rounded off while if Cp is too high, the square wave will overshoot So far we have talked about large DC voltages and high frequencies but if you have a circuit with high DC voltages and small signals, you need to switch the scope’s input to AC cou­ pling. This enables you to use high input sensitivity while blocking out a large quiescent DC voltage. As Fig.5 illustrates, the signals then must pass through the R1C1 time-constant. This will reduce the amplitude of low frequency signals, distort square waves and pulses and can play merry hell with pulse width modulation (PWM) signals. To see why, we need to critically look at just what it means to feed a signal through a coupling capacitor. In Fig.6 we have sketched a PWM signal which is applied to the left side of capacitor C1. Below that is the waveform which appears on the right hand side of C1 and is displayed on the oscilloscope screen. At time t7, the input signal lifts the left side of C1 from zero to +10V, charging the capacitor. So the right side also rises to +10V. Between times t7 and t8, the input voltage remains steady. But the charge on C1 leaks away through the resistor R1, lowering the voltage on the right hand side of the capacitor from +10V to +8V. Then at time t8, the input voltage drops from +10V to zero. Because this fall is abrupt, the potential on the right side of the capacitor must also fall by 10V; ie, from +8V to Fig.7: one possible circuit for the Chop/Alternate section of an analog scope. CMOS analog switches alternately switch the signals from channels 1 and 2 through to the vertical deflection amplifi­er. August 1996  69 Fig.8: this series of waveforms illustrates how the Chop mode in an oscilloscope rapidly chops between the input channels to produce two waveforms on the screen. Waveforms (c), (d) and (e) show an expansion of the 1ms period in waveforms (a) and (b). -2V, taking the displayed trace into negative regions. This may leak away to about -1.7V by time t9, when the input rises again. This time the +10V change in the input signal lifts the display up to +8.3V. During the long constant input between t9 and t10, the display again leaks down to +6.6V. You can see that the displayed waveform is far from the truth. When the positive input pulses are long, with a duty cycle greater than 50%, the display progressively migrates downwards (duty cycle is the ratio of the pulse on-time to the pulse off-time). If the duty cycle remained constant, after many cycles the displayed signal would be displaced until the area enclosed between the positive regions of the waveform and the zero line is equal to the area enclosed between the negative regions and the zero line. 70  Silicon Chip By this rule, the long duty cycle between times t7 and t12 will push the waveform downwards. But the same rule means that between times t13 and t16, when the duty cycle is short, the waveform display must rise above the zero line, in order to equalise positive and negative areas. So the complex PWM waveform of Fig.6 will rise and fall as the duty cycle changes. The only cure is to monitor the waveform with DC coupling. AC coupling is a trap for young players – use it only when you must block high DC voltages. Dual-trace operation One of the really powerful benefits of a scope is the ability to monitor two signals at once but here again there are traps. If you want to measure the timing or phase differences between two signals you need to know just how your scope displays two different inputs on the screen simultaneously. What we are talking about is the choice between Alternate and Chop modes. Fig.7(a) illustrates one possible circuit for the Chop/Alternate section of an analog scope. Two different signals on channels 1 and 2 firstly pass through their individual atten­uators and preamplifier stages A1 and A2, then to the Chop/Alter­ nate section which includes IC1, IC2 and IC3. You will easily follow its operation as we view it a bit at a time. IC1a, b and d are CMOS analog switches and each turns on only when a logic high signal is applied to its control terminal. For example, IC1a conducts between pins 4 and 3 only when a logic high is applied to pin 5. The timebase section of the oscilloscope, as well as pro­viding the horizontal sweep, also feeds a control signal in at point T. This controls all four CMOS switches via inverters IC2a, IC2b and IC2c. IC3 is a summing operational amplifier, while Ri1 and Ri2 are its two input resistors and Rf is the feedback resis­tor. Point X is the summing junction. The gain from either channel 1 or channel 2 inputs to the output at point N is -(Rf/Ri) = -(10kΩ/10kΩ) = -1. Signals from point N feed to the vertical deflection amplifier for display on screen. Now what happens when we select the Alternate display mode? Say we apply a signal to channel 1 input and a square wave to channel 2. If the timebase section feeds a low control signal to the point T, this will be inverted in IC2b and will present a logic high to pin 5 of gate IC1a, turning it on. So the sinewave signal on channel 1 will feed through A1, through Ri1, IC1a and IC3, and will pass on to the vertical deflection amplifier, to be displayed on the screen. At the same time, gate IC1b is off, so channel 2 signals cannot pass to the vertical deflection amplifi­er. But when a logic high signal is fed to point T, the condi­tions reverse. Analog switches IC1b and IC1c will conduct and IC1a turn off, allowing the channel 2 signal to be displayed on the screen. The control signal at point T is high on the 1st, 3rd, 5th, 7th, etc sweeps and low on the 2nd, 4th, 6th, 8th, etc. Thus, all odd sweeps display the sinewave on channel 1 and all even sweeps show the square wave on channel 2. You can use the individual vertical position (shift) con­trols to move the two displays apart. At slow sweep speeds, the display alternates between signal 1 in the upper half of the screen and signal 2 in the lower screen. At fast sweep speeds, the persistence of the screen phosphor enables you to see both signals continually on the screen. Hence, Alternate mode is successful with fast sweep speeds but unsuitable at slow sweeps. Chop mode Now what happens if you change to “Chop” mode. This causes a separate high frequency oscillator within the timebase unit to toggle the control signal fed to point T (toggle means to switch continually between logic high and low). This is done at a fixed fast rate, perhaps 10kHz, as illustrated in Fig.8 but in some high frequency osc­ illoscopes the toggle rate may be as high as 1MHz. In the example shown in Fig.8, the main sweep is switched to 100 mil- liseconds per division, which takes one second for each full sweep. The sinewave on channel 1 has a frequency of about 3.5Hz and the square wave on channel 2 is about 6Hz. The control signal at point T has period equal to 1/10kHz = 100µs as Fig.8 shows. This makes channel 1 conduct through IC1a for 50µs, channel 2 conducts through IC1b for the next 50µs and so on. Both input signals are thus chopped up into thousands of little time seg­ments 50µs long, like two lines of ants crawling across a page. On the screen are displayed these 20,000 discontinuous segments of the input signals, as IC1a and IC1b conduct in turn. A small sector of both traces is shown in Fig.8(d) & (e) drawn one thousand times time-expanded. While T is at logic high, a small segment of the sinewave (a) is displayed in the upper half of the screen. But when T is at logic low, a short piece of the square wave (b) appears on the lower half at (e). While one signal is displayed, the other is blanked off. This process continues repeatedly, right across the screen. The slight blur­ ring due to the width of the light spot makes each trace appear continuous. If we raised the sweep speed sufficiently we would see the discontinuous nature of the display. So chop mode is unsuitable for very fast sweep speeds. In some scopes Chop mode is automati­cally selected at slow time­ base speeds and Alternate is selected at high sweep speeds. Now we can see why Chop and Alternate modes can affect timing and phase comparisons between two different signals. Alternate mode leads to impossibly wrong results, because it allows the oscilloscope to trigger independently on each channel; time correlation is completely lost. Therefore, Chop mode must be used when comparing the timing of different signals. Phase shift A final vital point to note here is the phase shift which AC coupling produces, as noted above. Therefore, when comparing phases and timing of different signals, switch both channels to DC coupling or switch both channels to AC coupling. Don’t have channel 1 AC-coupled and channel 2 DC-coupled; that will lead to serious SC errors. 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