Пояснительная записка (1196146), страница 8
Текст из файла (страница 8)
Технические характеристики осциллографов GW Instekсерии GDS-200054Приложение Б. Analysis of oscilloscopes’ technical specifications2.1 BandwidthThe main task for any oscilloscope has been and still is an accurate reconstructionof the shape and amplitude of the original electrical signal. One of the main specifications of the modern digital storage oscilloscope is its bandwidth. Let us figure outhow this feature affects the waveform display quality and why the consumer canmake a mistake when choosing a device only considering the technical characteristics.Let us proceed to the bandwidth. This parameter is critical when choosing an oscilloscope and a digital storage oscilloscope (DSO) in particular.
A simplified blockdiagram of a DSO is shown in Figure 2.1.Figure 2.1 - Block diagram of DSOOscilloscope bandwidth is formed mainly by its analogue part - the input circuitsand the amplifier. Oscilloscope manufacturers sometimes directly indicate this parameter.The digital part of the device and its effect on the bandwidth is discussed below.Many users believe that the wider the bandwidth, the more authentically oscilloscopewill reproduce a waveform.
Let us define whether it is always true.Oscilloscope bandwidth is defined as the band starting from DC and ending on afrequency at which the amplitude of the input sine wave declines to -3 dB comparedto the original. Figure 2.2 shows an idealized frequency response of the oscilloscope.Thus, the frequency response of an oscilloscope is only specified to a cutoff frequen-55cy, and what happens to it at higher frequencies - is not always defined by the manufacturer.Figure 2.2 - The ideal frequency response of an oscilloscopeHowever, the modern developer for the most part has to deal with complex signals, so the choice based only on a bandwidth in no way can give a guarantee that itwill provide the correct displaying of these signals.Let us turn to the theory.
According to the fundamentals of spectral analysis, anysignal can be represented as the sum of its harmonic components. Figure 2.3 providesan illustration of a Fourier transform of the rectangular pulse in 3 odd-integer harmonics. It is obvious that having as many signal components as possible is necessaryfor a correct signal reconstruction. The number of harmonics with significant amplitudes is not limited by bandwidth of the device, and depends on the frequency response beyond the cutoff frequency.
That is, an oscilloscope with a bandwidth of NMHz and with a slope of the frequency response of -20 dB/decade will reconstructthe signal better than the device with the same bandwidth, but the with a slope of -40dB/decade. In this case, the first oscilloscope will obviously have a better dynamicperformance. Thus, the bandwidth only indicates that the amplitude of a sinusoidalsignal with a frequency corresponding to the upper frequency of the bandwidth is re-56duced by 29.3%. It is not specified how much the amplitude of higher frequencieswill reduce.Figure 2.3 – The Fourier decomposition of a rectangular pulse in three harmonicsLet us make an experiment – examining the square wave signal with a fundamental frequency of 10 MHz on GW Instek GDS-2062 and GDS-2202 oscilloscope models (specified bandwidth - 60 and 200 MHz, respectively), as well as when the 20MHz bandwidth limiter is on. G5-60 acts as a signal generator (the minimal PulseRepetition Time (PRT) - 0.1 ms, PRT installation error - ± 1 × 10-6 T, where T - a setPRT).
Connection circuit is shown in Figure 2.4. Loading is necessary for matchingthe low-impedance generator output (50 Ω) and the high-impedance input of the oscilloscope (1 MΩ).Figure 2.4 – Test circuit for examining square waves on the oscilloscopeThe Figure 2.5 shows that the waveform is hardly distorted in case of 200 and60 MHz bandwidths, but in the third case, the distortion is very noticeable - the thirdand fifth harmonic of the signal are suppressed by 20 MHz bandwidth.
Thus, it ispossible to deduce a "five times rule" - use an oscilloscope with a bandwidth at least57five times wider than the fundamental frequency of the test signal. This rule is especially revealing with square waves, triangle waves and sawtooth signals whose shapeis largely determined by the first five harmonics of their spectral composition.Figure 2.5 - 10 MHz square wave on oscilloscope with a bandwidth of: a) 200 MHz, b) 60 MHz,and c) 20 MHzLet us verify the bandwidths of these oscilloscopes.
To do this, connect the circuitas shown in Figure 2.6, and, adjusting the sine wave frequency in increments of 10MHz, register their output amplitude. The results are shown in Tables 2.1, 2.2 and2.3.Figure 2.6 - Test circuit for examining the oscilloscope bandwidth58Table 2.1 – Measurement results for 200 MHz modelf,MHz1102030405060708090A, V33.062.942.842.9832.982.963.12.84f,MHz100110120130140150160170180190A, V2.862.842.82.922.962.82.682.782.82.52f,MHz200210220230240250260270280290A, V2.22.142.181.981.71.581.541.41.181.06f,MHz300310320330340350360370380390A, V1.081.10.980.820.780.840.840.720.60.54f,MHz400A, V0.56Table 2.2 - Measurement results for 60 MHz modelf,MHz1102030405060708090A, V33.022.92.742.72.62.442.32.282.22f,MHz100110120130140150160170180190A, V2.11.941.841.81.71.541.41.341.281.04f,MHz200210220230240250A, V0.860.80.760.660.520.4259Table 2.3 - Measurement results for 20 MHz limiterf,MHz151015202530354045A, V32.942.722.482.242.061.921.861.81.76f,MHz50556065707580859095A, V1.741.71.661.621.641.641.661.61.651.66f,MHz100105110115120130140150160170A, V1.621.621.61.621.641.721.761.681.641.7f,MHz180190200A, V1.761.61.46Calculate the attenuation at the upper cutoff frequency using formula (2.1) for allthree cases: = 20 10 (),(2.1)where – the amplitude of the upper cutoff frequency; – the amplitude of the reference frequency (1 MHz).2.2) = −2.69397 32.44= 20 log10 () = −1.79463 32.24= 20 log10 () = −2.53746 3200 = 20 log10 (6020Amplitude losses in these cases are as follows:3 − 2.2) ∗ 100% = 26.7%33 − 2.44=() ∗ 100% = 18.7%33 − 2.24=() ∗ 100% = 25.3%3200 = (602060As one can see from the calculations, specifications guaranteed by the manufacturer are confirmed (Appendix A).
However, for measuring frequencies higher than100 MHz with an amplitude error of 5% one should use an oscilloscope with bandwidth exceeding 200 MHz. Otherwise, the high-frequency measurement is performedwith a significant amplitude error.2.2 Rise TimeThe next important parameter that determines the dynamic performance of an oscilloscope is the rise time.
Theoretically, amplitude, phase and transient characteristics of any dynamical system possess one-to-one correspondence [2]. However, dueto the high labor intensity and the high cost of obtaining detailed amplitude and phasecharacteristics plot (also known as Nyquist plot), in practice, a simplified formula 2.2is used for calculation of the rise time: =,(2.2)where = 0.35 - calculated constant (see below); – bandwidth, Hz; – the rise time in seconds.Incidentally, calculated rise time is often stated in oscilloscope specifications. Theconstant of 0.35 is obtained, provided that the mathematical model of the first-orderlow-pass filter is considered.
This means that the slope of the frequency responseabove the cutoff frequency should be -20 dB/decade. However, in the case of highfrequency correction circuit in the oscilloscope this formula is incorrect, since theslope of the frequency response in this case is not less than -40 dB/decade. In [3], theuse of this formula leads to errors in determining the required rise time and the valueof the constant can reach a value of 0.5.Thus, the estimated rise time does not provide full information on the dynamiccharacteristics of the oscilloscope, i.e. how accurately the device displays highfrequency signals, and how accurate the measurements of quantities such as, for example, the duration of the pulse, are.
And the rise times of oscilloscopes with thesame bandwidth may differ significantly from its calculated value.61Let us dwell on the issues of the high-frequency response correction in oscilloscopes. Building a precision input amplifier for oscilloscopes is quite a daunting task,so manufacturers have a desire to save money on the development and to compensatethe necessary bandwidth through the use of high-frequency correction. Previously,specific circuit solutions were used for this matter, however, the use of analogue correction circuits made it impossible to obtain a deep correction, and filter elements hadto be carefully selected. In addition, such filters have low thermal and temporal stability, resulting in the necessity of regular inspections.
With the advent of high-speeddigital signal processors (DSP) the problem was greatly simplified and the highfrequency correction based on digital (software) filters has been applied quite often.There are cases when due to the use of DSP, a line of oscilloscopes with bandwidthsup to 500 MHz was produced, which basically had oscilloscope with an analoguebandwidth of 200 MHz, or a DSO with a bandwidth of 6 GHz was implemented onthe basis of the analogue section with a bandwidth of about 4 GHz. However, such acorrection may unpredictably affect the frequency response of the oscilloscope abovethe bandwidth limit.
At the same time, manufacturers applying a correction do notspecify the bandwidth of analogue section separately.Let us check the rise time of the oscilloscope. Examine a rectangular pulse onDW Instek DSO to measure the time of the rising edge (test circuit is similar to Figure 2.4). The resulting edge is shown in Figure 2.7.Figure 2.7 – The rising edge of the rectangular pulse for rise time estimation62For accurate measuring, save the waveform on an external storage device and import it into MatLab computing environment (Figure 2.8).Figure 2.8 - The imported waveform in MatLabRise time is defined as time taken by a signal to change from 10% to 90% of themaximum absolute value.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
