Fullscreen HTML5Med Res (??MB)HTML4

Pt.9: Sampling Scopes For Ultra High Frequencies Typical digital scopes have a bandwidth which is limited to less than half their sampling rate. But a different design, known as sampling or digitising oscilloscope, is not limited by the sam­pler speed and can achieve a bandwidth as wide as 50GHz. By BRYAN MAHER So far in this series we have described many digital real time oscilloscopes and we have talked about the limitation of bandwidth which is related to the sampling rate. The reason such scopes are referred to as “real time” is that they can acquire sufficient samples in one pass of the input signal, from a single trigger, to show the waveform accurately. With this ability they faithfully display one-shot wave­ f orms and changing signals. By one pass of the input signal we mean the waveform accepted by the scope following one trigger event. The bandwidth of any oscilloscope is limited by two circuit sections. Firstly, there is the bandwidth lim78  Silicon Chip itation of the input analog circuits. Secondly, there is the Nyquist limit of the sampling circuitry and as discussed in previous chapters of this series, the Nyquist limit determines that this bandwidth limita­tion is always half the sampling rate. Hence, when operating in real time, a scope must sample more than twice as fast as the signal frequency and preferably, five or 10 times faster. That Nyquist factor means no scope can operate in real time with a bandwidth above about 2GHz, because present technology can’t sample faster than 8 billion samples per second (8GS/s). But a 2GHz bandwidth is not good enough for today’s mi­crowave and sat- ellite communications systems. Nor is it good enough for measurements on radar or fibre optic systems. That demands scopes with bandwidths between 3GHz and 50GHz. Such scopes can measure pulse risetimes and propagation delays in picoseconds! One picosecond (ps) is equal to one millionth of a microsecond (10-12). Oscilloscope risetime It’s a fact of life that every oscilloscope has a risetime of its own. That figure is intimately related to the scope’s bandwidth by the equation: Risetime = 0.35/Bandwidth. Naturally we use consistent frequency and time units, such as: seconds/Hertz or nanoseconds/GHz, etc. For example, a scope of 1GHz bandwidth has a risetime equal to (0.35/1GHz) = 0.35ns = 350ps. What does this mean in practice? Imagine we had some hy­pothetical pulse in which the voltage rises to full value in­stantly; ie, in no time at all (zero risetime). Suppose we dis­played that pulse on an oscilloscope which has 350ps risetime (1GHz bandwidth). In this case, the trace on the screen would take 350 picoseconds to rise from 10% to 90% of full height. We would therefore think that our pulse had a 350ps risetime, when in fact it hasn’t. We would be seeing the rise delays of the oscilloscope circuits, not the pulse. In many digital circuits, things happen so quickly that the system won’t work if the risetime of some pulses exceeds the design margin. Fig.1 shows the situation in typical tele­communi­cations equipment. They use ultra-fast synchronous digital ICs, where the bit rate is so high that pulses are somewhat rounded. The system clock tells each circuit when to interrogate a pulse line, to decide if that pulse is at logic 0 or logic 1 level. The aim is to examine the pulse close to its middle. In Fig.1(a) the pulse risetime is so fast that the voltage has risen above the logic 1 level before the clock circuits take a look, at time t1, t2, etc. So those pulses are correctly read as logic 1 every time. But Fig.1(b) shows a different case. Here, because of some fault condition, the pulse risetime is too slow. You’ll notice that when the system interrogates the pulse line at time t1, the pulse is still rising. It does not reach the logic 1 voltage level until a later time, w1. So that pulse is incorrectly read as a logic 0. And the next pulse in Fig.1(b) is also slow in rising but just reaches the logic 1 level at clock time t2. So any slight jitter in the pulse or clock timing could read that pulse cor­rectly as a logic 1 sometimes but erroneously as a logic 0 at other times. Also, the throughput or pulse propagation delay (time bet­ ween pulse into and out of an integrated circuit) must remain within prescribed limits. When things go wrong the technician or engineer must have an ultra-high bandwidth oscilloscope to measure these rises and delays in pico­seconds. Displayed risetime Every oscilloscope has its own risetime, so how are we to know the true value for an input pulse? The answer comes from the equation: Risetime displayed = √{(scope risetime)2 + (pulse risetime)2} You might say the presentation on the screen is always a stretched picture of the actual data pulse. In the particular case when the ri- Fig.1: fast rising pulses (a) reach logic 1 level before interrogation at clock times t1 and t2, so are read correctly. But slow rising pulse (b) reaches logic 1 level at later time w1, so is incorrectly read as a logic 0. setimes of pulse and scope are equal, then the screen displays a pulse rising nearly one and a half times slower than reality. Say the risetimes of both are equal to T picoseconds. Then: Displayed risetime = √(T2 + T2) = √(2T2) = 1.41T. No technician or engineer has time to sit and calculate the true risetime of every measurement, especially in a system break­down situation. The only practical solution is to use an ultra-wide bandwidth oscilloscope. This will have extremely fast inter­ nal risetime, miles faster than the get-up-and-go-time of the pulses to be measured. Pulse bandwidth Similarly every pulse has a bandwidth, related to its rise­time (or fall time, whichever is the faster) by an inversion of the previous equation: Bandwidth = 0.35/risetime. The practical meaning is that the bandwidth of any pulse tells us what bandwidth oscilloscope we need to display it, with errors of no more than 3dB and risetime stretch no more than 1.4 times. The bandwidth of a pulse bears no relation to its repeti­tion rate. For example, a slowly repeating pulse which rises extremely fast each time it does occur still requires a wideband scope to display it accurately. Ultra-wide bandwidth digital oscilloscopes are on the mar­ket, like the Hewlett Packard model HP54750A. With two HP54752A plug-ins, all four channels have a 50GHz bandwidth and a minus­cule 7ps internal risetime. The horizontal timebase speeds can be selected from 10ps/div to 1s/div. To achieve its enormous bandwidth, this scope uses a system called sequential equivalent time sampling, suitable for repeti­ tive signals only. This we’ll describe in a moment. The Autoscale control automatically sets vertical sensitiv­ity, offset scaling and timebase speed to display two cycles of the signal. It can capture 34 waveforms/second, each with 500 sample points. The maximum data record length is 4096 sample points per channel and the highest sampling rate is 40kS/s. The 12-bit A/D converter gives a vertical resolution of 4096 decision levels and averaging provides 15-bit words (32,768 decision levels). The display can resolve 256 points vertically and 451 points horizontally, in eight colour gradations. The intriguing question is how can any manufacturer make such ultra-wide bandwidth oscilloscopes when it’s impossible to sample anywhere near 50GS/s? We will now try May 1997  79 Fig.2: protection diodes D1 and D2 and the attenuator allow a scope to display large voltages or the amplifier A1 can raise small signals to viewable size. However, these components limit the scope’s analog bandwidth. to answer that question, albeit briefly. In the foregoing applications, usually the signals are waveforms repeating for many periods. This fact gives a luxury not enjoyed by real time digital scopes and opens up a whole new ball game. Provided we never want to display one-shots or fast chang­ing waveforms, continuously repeating signals allow a completely different design approach. For bandwidths from 2GHz up to 50GHz, manufacturers make two major changes. Design trade-offs In real time scopes, the stray shunt capacitances of the input protection diodes, attenuator and amplifier, shown in Fig.2, act to limit the analog bandwidth. To avoid this restric­ tion, the first change in designing ultra-wide bandwidth scopes is to just don’t use those components in the front end. That leaves the sampler right at the oscilloscope input terminal, as you can see in the simple block diagram of Fig.3. Next, a low bandwidth amplifier A2 is placed after the sam­pling bridge. This does not restrict the overall sys- tem band­width, because the sampler has converted the input signals to lower frequencies. With these changes we have an ultra-wide bandwidth front end but two trade-offs are inevitable. With no attenuator, we can only apply small signals to this type of scope. Typical sensitiv­ities range from 1mV/div to 250mV/div, with a maximum signal voltage of ±2V. Without any protection diodes, high voltages at the input can cause damage. Although an internal trigger takeoff is generally provided, the loading of this circuit does reduce the bandwidth. So usually the scope is triggered externally by the communications system clock. In describing real time digital scopes in this series, we have become familiar with samplers running much faster than the signal frequency; sampling speeds are typically between 200MS/s and 8GS/s. But in the quest for 50GHz bandwidth, aiming for even faster sampling speeds can’t work, because no sampler can be made to run twice as fast as 50GHz. But the sampling rate and band­width are intimately related only in real time oscilloscopes. In aiming for ultra-wide bandwidth, manufacturers replaced real time mode and high speed samplers with a completely differ­ent system. It is called “equivalent time sampling” and in this scheme there is no direct relation between sample rate and band­width. It comes in two types, known respectively as sequential and random. And always the signal must be repetitive. Sequential equivalent time In sequential equivalent time scopes, the sampling bridge in Fig.3 operates at relatively slow rates, typically 40kS/s to 200kS/s. And this speed bears no relation to the input signal frequency. To take each sample, the actual time the sampler switch remains momentarily closed is called the sampling interval. This can be as short as 10 femtoseconds (femto = 10-15). And that’s an incredibly short time for a switch to stay closed before it opens again. Often only one sample is taken following each trigger event. The scope Fig.3: to avoid loss of analog bandwidth, ultra-high frequency sampling scopes place the sampler right at the input terminal. But this restricts the range of input voltages to about ±2V. 80  Silicon Chip might be triggered 4000 or 40,000 times each second, running until it accumulates hundreds or thousands of samples into the memory (RAM). This process is illustrated in the example shown in Fig.4. Nothing happens until the scope is triggered. Then 0.1ps after the first trigger event the first very short sample is taken. It is amplified and immediately digitised in the A/D converter and the resultant digital data is stored in RAM. While all that converting and data storing was being done, the scope was not ready to be triggered again, so many thousands of cycles of the analog signal will pass in the circuit unseen. But this is not a problem because we are assuming that the signal is repetitive. When the trigger circuit eventually rearms, the next trig­ger is accepted and 0.2ps later sample number 2 is acquired, amplified, digitised and stored in the RAM, as illustrated in Fig.4. Next, 0.3ps after the third accepted trigger event, sample number 3 is taken and similarly converted to a digital word which is placed in the RAM. And so on. Each time the oscilloscope triggers, it takes one more sample, always at a longer time after the trigger. We illustrate this process in Fig.4 but show only 10 points for simplicity (in reality between 500 and 5000 are taken). When the RAM contains enough samples or if the trigger ceases, or if the operator tells it to halt, the scope stops sampling. Now the display microprocessor sorts out all those digitised samples held in the memory. It reassembles them all onto the screen as a lot of bright points, as in Fig.5, in the same order as they were taken. That’s why this is called sequen­tial equivalent time sampling. The horizontal coordinate of each is proportional to the time increment after the respective trigger event for that sample was taken. The vertical coordinate is proportional to the value of the digital word, which reflects the analog voltage of each sample. Fig.4: in sequential equivalent time sampling, ultra-high frequen­cy oscilloscopes take just one sample each time the scope is triggered. At each signal pass, the timing between trigger and sample is progressively incremented. Equivalent sampling rate If 500 trigger events occur and after each one sample is taken, we will have 500 samples of the signal all digitised and stored in memory. Each sample was taken 0.1ps later after the respective trigger than the previous sample. Fig.5: after accumulating hundreds or thousands of samples, the scope reassembles them all in one display to represent the re­petitive signal waveform. May 1997  81 The ultra-high frequency Hewlett Packard HP54750A scope with plug-ins provides up to four 50GHz channels. Feedback A/D converters yield 12-bit digital words or 15 bits with averaging. Horizontal resolution is 62.5fs, with 8ps time interval accuracy. The maximum sampling rate is 40kS/s. The horizontal timebase ranges from 10ps/div to 1s/div. So the 500th sample was taken 50ps after the 500th trigger. That means the whole screen display represents 50 picosec­onds of the live input signal. As there are 10 major horizontal divisions across the screen, we call the display timebase 5ps/div, the equivalent horizontal resolution of this sampling oscilloscope. When displayed on the screen we’ll have 50 sample points per horizontal division, each represented as a bright point of light. They’ll be close enough together to look like a continuous trace. Of course nothing in the display is actually moving any­where near 5ps/ div speed. We know from previous chapters that the trace on the screen is redrawn at the slow rate of 60 times per second. The display only represents 50 sample points per 5ps. But what you see on the screen is equivalent to a scope running at the impossible speed of 500 samples every 50 picosec­onds, or 10,000GS/s. This is the equivalent sampling rate. No real time scope can take samples at anything like that speed but an equivalent time oscilloscope doesn’t 82  Silicon Chip have to. It just reassembles all those samples into a display which appears to have that stupendous sampling rate. If the screen in Fig.5 displays two cycles of the input signal, it must be that the analog input has a real period of 50ps/2, meaning a frequency of 40GHz. But we assumed before that the scope was being triggered 40,000 times per second. That means the sampler is running at only 40kS/s. So after each sample is taken, about a million cycles of the signal flow through the circuit before the scope is again triggered and the next sample taken. So the two cycles displayed on the screen are representative of 500 million signal cycles. Now we see why the analog input must be repetitive for equivalent time scopes. To emphasize this aspect, these ultra-high bandwidth in­struments are known as a sampling (or digitizing) equivalent time scopes. No aliasing Provided a suitably fast sweep speed is chosen, there are so many sample points per cycle of the in- put signal that no alias ghosts will appear on the screen. By this means the Nyquist frequency limit can be exceeded and aliasing avoided. But too slow a sweep speed could restrict the number of samples taken so that aliasing could invade the display. By using this equivalent time sampling system, a scope which samples at only 40kS/s can quite successfully display 50GHz signals! As a bonus, this slower sampling rate allows designers to use high accuracy 12-bit or 14-bit feedback A/D converters, which provide 16,384 decision levels in the digitisation. This allows mathematical operations of great accuracy and eliminates steps in the screen display. There’s more to this story but we must leave it until the next (and final) chapter of this series. References (1). HP54750 reference book: HP publications 5091-3756E and 5952-0163. (2). Tektronix publications 47W-7520, 85W-8306, 85W-8308, 47W-7209. SC Acknowledgement Thanks to Tektronix Australia and Hewlett Packard Austra­lia and their staff for data and illustrations.