ELE 211: Electronic and Electrical Measurements Lecture 5 PDF

ELE 211: Electronic and Electrical Measurements Dr. Wael Taha Lecture 5: Frequency and Capacitance Measurement Digital frequency meter (DFM) based on straight counting. The digital frequency meter illustrated in Figure 1 consists of an accurate timing...

ELE 211: Electronic and Electrical Measurements Dr. Wael Taha Lecture 5: Frequency and Capacitance Measurement Digital frequency meter (DFM) based on straight counting. The digital frequency meter illustrated in Figure 1 consists of an accurate timing source (or time base), digital counting circuits, circuitry for shaping the input waveform, and a circuit for gating the shaped waveform to the counter. The input is first amplified or attenuated, as necessary, and then fed to the wave-shaping circuit, which converts it into a square or pulse waveform with the same frequency as the input. The presence of this wave-shaping circuit means that the input can be sinusoidal, square, triangular, or can have any other repetitive-type waveform. The shaped waveform is fed to one input terminal of a two-input AND gate, and the other AND gate input is controlled by the ܳ output from a flip-flop. Consequently, the pulses to be counted pass through the AND gate only when the flip-flop ܳ terminal is high. Figure 1 Basic block diagram and waveforms for a digital frequency meter. Cycles of the fre- quency to be measured are counted over a known time period. One thousand cycles counted over a period of 1s gives a 1 kHz measured frequency. 1  The flip-flop is controlled by the timing circuit, changing state each instant that the timer output waveform goes in a negative direction (a negative-going edge). When the timing circuit output frequency is 1 Hz, as illustrated, the flip-flop ܳ output terminal is al- ternately high for a period of 1 s and low for 1 s. In this case, the counting circuits are toggled (by the pulses from the wave-shaping circuit) for a period (termed the gate time) of 1 s, and the total count indicates the frequency directly in hertz. The counting circuits are reset to the zero-count condition by the negative-going edge of the ܳത output from the flip-flop, so that the count always starts from zero. As in the case of the digital voltmeters, latch or display enable circuits are employed to make the digital display readable. The latch circuits are briefly triggered at the end of the counting time by the positive-going edge of the flip-flop ܳത output. The display is corrected at this instant (if necessary), and then remains constant until the next latch trigger input. Range changing Flip Flops can be configured to divide the frequency of the input signal by 2, as shown in Figure 2. In a similar manner, decade counters divide the frequency of the input signal by 10, as clarified in Figure 3. As indicated in this figure, accurate time periods of 10 ߤ‫ݏ‬, 100 ߤ‫ݏ‬, 1 ݉ ‫ݏ‬, 100 ݉ ‫ݏ‬, 1 ‫ݏ‬, and so on, can be produced by the use of a crystal oscillator and several decade counters. Such a time base can be used with a digital frequency meter to give several ranges of frequency measurement. Figure 4 shows a switching arrangement for the selection of time period and ଵ decimal point. When a 1 s time period is used for counting the input pulses, the 3 ଶ digit display might have a Hz unit identification alongside it, as illustrated. Alternatively, as shown in Figure 5 (a), the frequency units could be identified as kHz if a decimal point is included after the first numeral. Now consider the effect of using a 100 ݉ ‫ݏ‬counting time instead of a 1 ‫ ݏ‬time peri- od. A display of 1999 indicates 1999 cycles of input waveform per 100 ݉ ‫ݏ‬, or 19.99 kHz [Figure 5(b)]. Thus, when the time base is switched to 100 ݉ ‫ݏ‬, the decimal point must also be switched. Similarly, if the time base is switched to 10 ݉ ‫ݏ‬, the decimal point is moved right once again, so that the maximum measurable frequency is 199.9 kHz [Figure 5(c)]. A further switch of the time base to a period of 1 ݉ ‫ ݏ‬gives a maximum pulse count of 1999 pulses per 1 ݉ ‫ݏ‬, or 1.999 MHz [Figure 5 (d)]. 2 Figure 2 Frequency division using Flip Flops, each Flip flop divide the input frequency by 2. 3 Figure 3 Frequency division using decade counters, each decade counter divide the input frequency by 10. Figure 4 A switching arrangement for the selection of time period and decimal point. 4  Figure 5 The decimal point and units display are selected according to the time period. Example 1 A digital frequency meter has a time base derived from a 1 MHz clock generator fre- quency-divided by decade counters. Determine the measured frequency when a 1.512 kHz sine wave is applied and the time base uses (a) six-decade counters and (b) four- decade counters. Solution (a) Using six-decade counters ଵ ெ ு௭ Time base frequency ݂ଵ = ଵ଴ల = 1 ‫ݖܪ‬ ଵ Time period, ‫ݐ‬ଵ = ଵ ு௭ = 1‫ݏ‬ Cycles counted ݊ଵ = (݅݊‫ݐ × )ݕܿ݊݁ݑݍ݁ݎ݂ݐݑ݌‬ଵ = 1.512 ݇‫×ݖܪ‬ 1‫ݏ‬ ݊ଵ = 1512 ܿ‫ݏ݈݁ܿݕ‬ Measured frequency, ݂ = 1.512 ݇ ‫ݖܪ‬ 5 (b) Using four-decade counters ଵ ெ ு௭ Time base frequency ݂ଶ = = 100 ‫ݖܪ‬ ଵ଴ర ଵ Time period, ‫ݐ‬ଶ = = 10 ݉ ‫ݏ‬ ଵ଴଴ ு௭ Cycles counted ݊ଶ = (݅݊‫ݐ × )ݕܿ݊݁ݑݍ݁ݎ݂ݐݑ݌‬ଶ = 1.512 ݇‫×ݖܪ‬ 10 ݉ ‫ݏ‬ ݊ଶ = 15 ܿ‫ݏ݈݁ܿݕ‬ Measured frequency, ݂ = 1.5 ݇ ‫ݖܪ‬ The partial pulses that get through the AND gate may or may not succeed in triggering the counting circuits. So, there is always a possible gating error of ± 1 cycle in the count during the timing period. This (one count) is defined as the least significant digit (LSD). The accuracy of a digital frequency meter is usually stated as ± 1 ‫ ܦܵܮ‬± time base error Errors in the time base generated by a crystal-controlled oscillator are normally the result of variations in temperature, supply voltage changes, and aging of crystals. With reasonable precautions, the total time base error might typically be < 1 x 10-6, or less than 1 part in 106. The total measurement error depends on the actual frequency measured. Example 2 A frequency counter with an accuracy of ± 1 ‫ ܦܵܮ‬± (1 × 10ି଺) is employed to measure frequencies of 100 Hz, 1 MHz, and 100 MHz. Calculate the percentage measurement error in each case. Solution At ݂ = 100 ‫ݖܪ‬, ݁‫ = ݎ݋ݎݎ‬± (1 ܿ‫ݐ݊ݑ݋‬+ 100 ‫ × ݖܪ‬10ି଺) = ± (1 ܿ‫ݐ݊ݑ݋‬+ 1 × 10ିସ ܿ‫)ݏݐ݊ݑ݋‬ ≈ ± 1 ܿ‫ݐ݊ݑ݋‬ 1 % ݁‫ = ݎ݋ݎݎ‬± ൬ × 100%൰ 100 ‫ݖܪ‬ % ݁‫ = ݎ݋ݎݎ‬± 1% 6  At f = 1 MHz, ݁‫ = ݎ݋ݎݎ‬± (1 ܿ‫ݐ݊ݑ݋‬+ 1 ‫ × ݖܪ ܯ‬10ି଺) = ± (1 ܿ‫ݐ݊ݑ݋‬+ 1 ܿ‫)ݐ݊ݑ݋‬ ≈ ± 2 ܿ‫ݐ݊ݑ݋‬ 2 % ݁‫ = ݎ݋ݎݎ‬± ൬ × 100%൰ 1 ‫ݖܪ ܯ‬ % ݁‫ = ݎ݋ݎݎ‬± 2 × 10ିସ% At f = 100 MHz, ݁‫ = ݎ݋ݎݎ‬± (1 ܿ‫ݐ݊ݑ݋‬+ 100 ‫ × ݖܪ ܯ‬10ି଺) = ± (1 ܿ‫ݐ݊ݑ݋‬+ 100 ܿ‫)ݐ݊ݑ݋‬ ≈ ± 101 ܿ‫ݐ݊ݑ݋‬ 101 % ݁‫ = ݎ݋ݎݎ‬± ൬ × 100%൰ 100 ‫ݖܪ ܯ‬ % ݁‫ = ݎ݋ݎݎ‬± 1.01 × 10ିସ% The previous example shows that at a frequency of 100 Hz the error due to ±1 count is ±1%, while that due to the time base is insignificant. At 1 MHz, the error due to one count is equal to that due to the time base. At 100 MHz, the time base is responsible for an error of ±100 counts, although the total error is still a very small percentage of the measured frequency. Therefore, at high frequencies the time base error is larger than the ±1 count error, while at low frequencies the ±1 count error is the larger of the two (see Figure 6). At frequencies lower than 100 Hz, the percentage error due to ±1 count is greater than 1 %, so the greatest measurement error occurs at low frequencies. The low- frequency error can be greatly reduced by the reciprocal counting technique. 7 Figure 6 The counting error (as a number of cycles) that results from the time base error is largest when measuring a high frequency. DFM based on reciprocal counting In the rearranged frequency meter system shown in Figure 7, the 1 MHz oscillator fre- quency from the time base is applied directly to the AND gate in place of the output from the wave-shaping circuit. The reshaped input wave (which is to have its frequency measured) is employed to toggle the flip-flop. As illustrated by the waveforms, this arrangement results in the AND gate passing pulses from the 1 MHz oscillator to the counting circuits during the time period (T) of the input wave. when a 100 Hz input wave to be measured is applied, the AND gate will pass the pulses for a time period of 1 / 100 Hz = 10 ms and the time period of each cycle from 1 MHz oscillator is 1 ߤs. Hence, during time period T, the number of counted pulses ݊ is given as: ݊ = 10 ms /1 ߤs = 10000 ଵ which is displayed as 10000 μs and its reciprocal determines the frequency (A 4 digit ଶ display should be used). The accuracy of measurement of the 100 Hz frequency is now ±1 count in 10000, or 1 % ݁‫ = ݎ݋ݎݎ‬± ൬ × 100%൰ 10000 % ݁‫ = ݎ݋ݎݎ‬± 0.01% 8 A 0.01% error is a big improvement over the 1% error that occurs with the straight counting technique (see Example 2). The accuracy improvement with the reciprocal counting. method is even better at frequencies lower than 100 Hz. For high-frequency measurements, the straight counting method gives the most accurate result. Figure 7 Digital frequency meter system rearranged for reciprocal counting. The time period of low-frequency inputs can be accurately measured by counting the clock pulses during the period. Capacitance measurements on Digital Multimeters Some digital multimeters have a facility for measuring capacitance. This normally involves charging the capacitor at a constant rate, and monitoring the time taken to arrive at a given terminal voltage. In the ramp generator digital voltmeter system in Figure 1 in the previous lecture, the ramp is produced by using a constant current to charge a capacitor. Figure 8 shows the basic method. Transistor ܳଵ, together with resistors ܴଵ, ܴଶ, and ܴଷ produce the constant charging current to capacitor ‫ܥ‬ଵ, when ܳଶ, is off. ‫ܥ‬ଵ, is discharged when ܳଶ switches on. 9 Figure 8 Capacitance measurement using digital instrument. As already explained for the digital voltmeter, a ramp time (‫ݐ‬ଵ) of 1 s and a clock generator frequency of 1 kHz result in a count of 1000 clock pulses, which is then read as a voltage. If ܸ௜ remains fixed at 1 V, the display could be read as a measure of the capacitor in the ramp generator. A 1 ߤ‫ ܨ‬capacitor might produce the 1 s counting time, so that the display is read as 1.000 ߤ‫ܨ‬. A change of capacitance to 0.5 ߤ‫ ܨ‬would give a 0.5 s counting time and a display of 0.500 ߤ‫ܨ‬. Similarly, a capacitance increase to 1.5 F would produce a 1.5 s counting time and a 1.500 ߤ‫ ܨ‬display. In this way, the digital voltmeter is readily converted into a digital capacitance meter. References: David A. Bell, Electronic Instrumentation and Measurements, second edition. 10