High-Speed ​​Time Domain Measurements—Practical Tips for Improvement

Making accurate high-speed time domain measurements can be difficult, but finding information that can help improve your measurement methods is not. Understanding the basic principles of oscilloscopes and probes is always useful, but there are a few additional tricks of the trade and some good old-fashioned engineering common sense that can help you get fast and accurate results. Here are some tips and techniques that I have learned over the past 25 years. Applying even one or two of these techniques to your measurement approach will help improve your results.

You can't simply move an off-the-shelf oscilloscope and grab a random probe from the drawer for high-speed measurements. When choosing the right oscilloscope and probe for high-speed measurements, the first things to consider are: signal amplitude, source impedance, rise time, and bandwidth.

Selecting an Oscilloscope and Probe

There are hundreds of oscilloscopes available, ranging from very simple portable oscilloscopes to dedicated benchtop digital storage oscilloscopes that cost hundreds of thousands of dollars (some high-end probes can cost more than $10,000 themselves). There are also many different types of probes that match these oscilloscopes, including passive, active, current measurement, optical measurement, high voltage measurement, and differential signal measurement probes. A comprehensive description of every type of oscilloscope and probe available is beyond the scope of this article, so we will focus on oscilloscopes suitable for high-speed voltage measurements using passive probes. The oscilloscopes and probes discussed here are generally used to measure signals with broadband and short rise time characteristics. In addition to these specifications, we also need to know the sensitivity of the circuit to loads, including resistive loads, capacitive loads, and inductive loads. For example, when using a large capacitance probe, measuring a signal with a fast rise time will produce distortion; in some applications, the circuit will not allow the probe to be inserted into it at all (for example, some high-speed amplifiers will produce oscillations when a capacitor is placed at its output). Knowing the limits and expectations of the circuit will help you choose the right oscilloscope and probe combination and the best way to use them.

First, signal bandwidth and rise time will limit the choice of oscilloscope. A general rule of thumb is that the bandwidth of the oscilloscope and probe should be at least three to five times the bandwidth of the signal to be measured.

bandwidth

Whether the signal to be measured appears in an analog or digital circuit, the oscilloscope needs to have sufficient bandwidth to reproduce the signal faithfully. For analog signal measurements, the highest frequency of the signal to be measured will determine the bandwidth of the oscilloscope. For digital signal measurements, it is usually the rise time—not the repetition rate—that determines the required oscilloscope bandwidth.

The -3 dB frequency is generally used to represent the bandwidth of an oscilloscope. The amplitude of the sine wave displayed at -3 dB drops to 70.7% relative to the maximum input amplitude, that is,

(1)

It is critical to ensure that the oscilloscope has sufficient bandwidth to minimize errors. Frequency measurements should never be made near the -3 dB bandwidth of the oscilloscope, as this will automatically introduce a 30% amplitude error when measuring a sine wave. Figure 1 shows a typical degradation curve of amplitude accuracy as the ratio of the signal frequency to the oscilloscope bandwidth changes.

Figure 1. Amplitude attenuation curve

For example, a 300 MHz oscilloscope will have an error of up to 30% when measuring a 300 MHz frequency. To keep the error below 3%, the maximum signal bandwidth it can measure is about 0.3×300 MHz, or 90 MHz. In other words, to accurately measure a 100 MHz signal (<3% error), you need an oscilloscope with at least 300 MHz bandwidth. The attenuation curve in Figure 1 illustrates a key point: To keep the amplitude error reasonable, the bandwidth of the oscilloscope and probe combination should be at least 3 to 5 times the bandwidth of the signal to be measured. To ensure that the amplitude error is less than 1%, the bandwidth of the oscilloscope should be at least 5 times the bandwidth of the signal.

For digital circuits, rise time is particularly important. To ensure that the oscilloscope will faithfully reproduce the rise time, the expected rise time can be used to determine the bandwidth requirements of the oscilloscope. This relationship assumes that the circuit responds like a single-pole, low-pass RC network, as shown in Figure 2.

The output voltage in response to an applied voltage step signal can be calculated using equation (2).

(2)

The rise time of a step response is defined as the time it takes for the output amplitude to rise from 10% to 90% of the step amplitude. Using equation (2), the time for a 10% step amplitude is 0.1 RC, and the time for a 90% step amplitude is 2.3 RC. The difference between them is 2.2 RC. Since the -3 dB bandwidth (f) is equal to 1/(2π RC), and the rise time (tr) is equal to 2.2 RC, then

(3)

Therefore, for a single-pole probe response, we can use equation (3) to calculate the equivalent bandwidth of the signal if the rise time is known. For example, if the rise time of the signal is 2 ns, the equivalent bandwidth is 175 MHz.

(4)

To maintain a 3% error, the bandwidth of the oscilloscope and probe should be at least 3 times the bandwidth of the signal to be measured. So a 600 MHz bandwidth oscilloscope should be used to accurately measure a 2 ns rise time.

Probe construction

The probe is a remarkable device considering its simplicity. It consists of a probing tip (which contains a parallel RC network), a length of shielded wire, a compensation network, and a ground clip. The most important requirement of a probe is to provide a non-intrusive interface between the oscilloscope and the circuit under test—disturbing the circuit as little as possible while allowing the oscilloscope to reproduce the signal under test almost perfectly.

In the past, in order to measure gate and plate voltages, high impedance was required to reduce the load on the signal nodes. So the probe was placed in a vacuum chamber for a few days and then removed when the measurement was started. This principle is still very important today. High impedance probes do not add too much load to the circuit under test, and therefore provide an accurate waveform of the real signal at the measurement node.

In my lab experience, the most commonly used probes are 10x and 1x passive probes; 10x active field effect transistor (FET) probes are the next most commonly used. The 10x passive probe reduces the signal to one-tenth of its original value. The 1x probe has no attenuation and can measure the signal directly. It has a 1MΩ input impedance and the capacitance at the probe tip is as high as 100 pF. Figure 3 shows a typical schematic of a 10x attenuation, 10 MΩ probe.

Figure 3. Probe schematic diagram

Rp (9 MΩ) and Cp are located inside the probe tip, R1 represents the oscilloscope's input impedance, and C1 represents the combined value of the oscilloscope's input capacitance and the probe's compensation box capacitance. For accurate measurements, the two RC time constants (RpCp and R1C1) must be equal; any imbalance will introduce rise time errors and amplitude errors. Therefore, it is important to always calibrate the oscilloscope and probe before making a measurement.

calibration

The first thing you should do after getting a working oscilloscope and probe is to calibrate the probe to ensure its internal RC time constants match. Do not calibrate too often, as it is not necessary.

Figure 4 shows how to properly connect the probe to the probe compensation output of the oscilloscope. Use a non-magnetic adjustment tool to adjust the adjustment screws in the compensation box to complete the calibration until a flat waveform response is observed.

Figure 4. Calibrate the oscilloscope probe.

FIG5 shows the waveforms produced by the probe under compensation, over compensation and proper compensation.

Note that under-compensation and over-compensation can introduce large rise time and amplitude measurement errors. Some oscilloscopes have built-in correction. If your oscilloscope has built-in correction, be sure to calibrate it before taking measurements.

(a)	(b)	(c)

Figure 5. Probe compensation: (a) undercompensation; (b) overcompensation; (c) proper compensation

Ground clamp and high-speed measurement

The inherent parasitic inductance of the ground clip makes it mutually exclusive with actual high-speed measurements. Figure 6 shows the principle schematic diagram of an oscilloscope probe and ground clip. The probe LC combination forms a series resonant circuit - the resonant circuit is the basis of the oscilloscope.

Figure 6. Equivalent probe circuit

This added inductance is not a desirable characteristic because the series LC combination can add significant overshoot and ringing to an otherwise clean waveform. This overshoot and ringing is often not noticeable because of the limited bandwidth of the oscilloscope. For example, if a signal containing a 200 MHz oscillating waveform is measured with a 100 MHz bandwidth oscilloscope, we will not see the ringing because the signal is greatly attenuated by the oscilloscope's bandwidth. Remember that for a 100 MHz bandwidth oscilloscope, Figure 1 shows a 3 dB attenuation at 100 MHz, with a continuous 6 dB drop per octave. Therefore, the 200 MHz parasitic ringing will drop by nearly 9 dB, reducing it to about 35% of the original signal amplitude, making it difficult to see. However, as oscilloscope measurement speeds increase and bandwidths increase, the effects of the ground clamp can be clearly seen.

The oscillation frequency introduced by the ground clamp can be estimated by calculating the series inductance of the ground clamp using formula (5). L represents the inductance in nanohenry (nH), l represents the wire length in inches (in), and d represents the wire diameter in inches (in).

(5)

Then substitute the result of formula (5) into formula (6) to calculate the resonant frequency f (Hz). L represents the ground clip inductance in Henry (H), and C represents the total capacitance of the probing node (F) - the combination of the probe capacitance and any parasitic capacitance.

(6)

Here are a few examples of using ground clips with different lengths of wire. In the first example, an 11 pF probe with a 6.5 in ground clip is used to measure a fast rising pulse edge. The measurement results are shown in Figure 7. At first glance the pulse response looks clean, but a closer look reveals a low amplitude 100 MHz decaying ring.

Figure 7. Measurement results using a 6.5 in ground clip

Now let's use equations (5) and (6) to express the physical properties of the probe to check if this 100 MHz oscillation is generated by the ground pin. The ground clip is 6.5 inches long and the wire diameter is 0.03 inches; this results in an inductance of 190 nH. Substituting this value into equation (6), and C = 13 pF (11 pF oscilloscope probe capacitance and 2 pF stray capacitance) results in an oscillation of approximately 101 MHz. This close correlation with the observed frequency allows us to conclude that the 6.5-inch ground clip is the cause of the low-amplitude oscillation.

Now consider a more extreme case where a fast signal with a 2 ns rise time is applied. This is common on many high-speed PC boards. Figure 8a shows the large overshoot and extended ringing observed using a TD2000 Series oscilloscope. The reason is that the fast rise time of 2 ns and the equivalent bandwidth of 175 MHz has enough energy to stimulate the 100 MHz series LC of the probe lead to ring. The overshoot and ringing are about 50% peak-to-peak. This effect from typical grounding can be clearly seen and is completely unacceptable in high-speed measurements.

Removing the ground pin allows a more realistic view of the waveform in response to an applied input signal (see Figure 8b).

Preparing the probe for high-speed measurements

为了获得有意义的示波器测量波形，我们需要去掉地线夹电路并且要拆卸探头。一定要要对探头做正确地拆卸！要拆除的第一个 部件是按压式探头尖端适配器。接下来，旋开包在探头尖端外面的塑料套筒。然后要拆除的是地线夹。图9示出示波器探头改进前（a）和改进后（b）的探头外 形。图9（c）示出使用6 in地线夹测量脉冲发生器的上升沿；图（d）示出使用为高速测量准备的探头〔见图9（b）〕做相同测量的测量结果。如图8所示，改进的测量结果非常显著。

(a)	(b)

Figure 8. (a) Step response with a 2 ns rise time measured with a 6.5 in ground clip; (b) step response without the ground clip.

(a)	(b)
(c)	(d)

Figure 9. (a) Unmodified probe taken out of the box; (b) Probe modified for high-speed measurement; (c) Measurement results using the unmodified probe; (d) Measurement results using the modified probe.

(a)

(b)

(c)

Figure 10. Method for removing the grounding of the oscilloscope probe.

接下来，为了校准需要直接拆卸探头（见图4）。一旦完成校准，探头就可以准备使用了。探头直接靠近某个测试点同时将探头 的金属外套连接一个局部接地。关键是如何在示波器探头外套上做恰当的接地连接。这样可消除使用探头地线夹引入的串联电感。图10a示出使用改进探头的正确 测量方法。如果探头直接接地很不方便，可以使用一付金属镊子、一把小螺丝刀或甚至一个改进地线连接的纸夹子，如图10b所示。可以将一段短的裸线在探头的 金属外套上绕几圈（地线环），如图10c所示，从而可提高测量灵活性并且能够测量多点（在小范围内）。

A better approach, if feasible, is to design dedicated high-frequency test points on the PCB board (see Figure 11). This probe tip adapter provides all the advantages of using a bare probe tip as described above, allowing many test points to be measured quickly and accurately.

Figure 11. PCB-to-probe tip adapter

Capacitive Effects of Probes

Probe capacitance can affect rise time and amplitude measurements; it can also affect the stability of some devices.

The probe capacitance directly increases the capacitance of the node being measured. The additional capacitance increases the time constant of that node, slowing down the rise and fall of the pulse. For example, if a pulse generator is connected to an arbitrary capacitive load, where CL = C1, as shown in Figure 12, then the associated rise time is calculated using equation (7), where Rs (= R1, see Figure 12) is the impedance of the signal source.

(7)

Figure 12. Rise time determined by RC load.

If Rs = 50Ω, CL = 20 pF, then tr = 2.2 ns.

Next, let’s consider measuring the same circuit using a probe with a 10 pF capacitance and a 10:1 attenuation ratio. The new circuit is shown in Figure 13. The total capacitance is now 31 pF and the new rise time is 3.4 ns, a 54% increase in rise time! Clearly this is unacceptable, but are there other options?

Figure 13. Additional probe capacitance

Active probes are another good choice for measuring high-speed circuits. Active probes or FET probes contain an active transistor (usually a FET) that can amplify the signal, while passive probes can only attenuate the signal. The advantages of active probes are extremely wide bandwidth, high input impedance, and low input capacitance. Another solution for measuring high-speed circuits is to use an oscilloscope probe with a high attenuation ratio. Generally, increasing the attenuation ratio of a probe will reduce its capacitance.

Capacitance at the probe tip can not only cause errors when measuring rise times, but can also cause some circuits to produce overshoot and ringing, or in extreme cases, to become unstable. For example, many high-speed op amps are sensitive to the effects of capacitive loading at their output and inverting input. When additional capacitance is introduced at the output of a high-speed amplifier (in this case, the oscilloscope probe tip), the amplifier’s output impedance and additional capacitance form an additional pole in the feedback response. This pole creates a phase shift and reduces the amplifier’s phase margin, which can lead to instability. This loss of phase margin can cause ringing, overshoot, and ringing. Figure 14 shows a Tektronix P61131 oscilloscope probe with 10 pF capacitance and 10:1 attenuation, and proper high-speed grounding, measuring the output of a high-speed amplifier. The signal produces an overshoot of 1300 mV with 12 ns of ringing. Clearly, this probe is not suitable for this application.

Figure 14. Measuring the output of a high-speed amplifier using a 10 pF probe.

Fortunately, there are several solutions to this problem. First, you can use a lower capacitance probe. In Figure 15, the same measurement as in Figure 14 was made using a Tektronix P6204 1.1 GHz oscilloscope with a 1.7 pF capacitance 10:1 attenuation FET active probe, again using proper high-speed grounding.

Figure 15. Measuring the output of a high-speed amplifier using a 1.7 pF FET active probe.

在这种情况中，使用较低电容的有源探头显著减小了过冲（600 mV）和振荡时间（5 ns）。另外一种方法是加入一个很小的与示波器探头串联的电阻（通常是25 Ω～50 Ω）。这有助于将探头电容与放大器的输出隔离，并且减小振荡和过冲。

Propagation Delay

A simple way to measure propagation delay is to measure both the input and output of the device under test (DUT) simultaneously. Propagation delay is easily read from the oscilloscope's display as the time difference between the two waveforms.

However, when measuring short propagation delays (<10 ns), care must be taken to ensure that both probes on the oscilloscope are the same length. Since the propagation delay of a wire is approximately 1.5 ns/in, two probes of different lengths can produce considerable error. For example, using a 3-foot (ft) probe and a 6-ft probe will produce a signal propagation delay error of approximately 4.5 ns — a significant error when making single-digit or double-digit nanosecond (ns) measurements.

If you do not have two probes of equal length (which is often the case), proceed as follows: Connect both probes to the same signal source (such as a pulse generator) and record the difference in propagation delay, called the “cal factor.” The “cal factor” is then subtracted from the reading of the longer probe, thus calibrating the measurement.

in conclusion

Although high-speed measurements are not overly complex, there are many factors that must be considered when venturing into the lab to make high-speed time domain measurements. Oscilloscope bandwidth, calibration, rise time, and probe selection as well as probe tip and ground lead length all play a role in the quality and integrity of the measurement. Using some of the techniques presented here can help speed up the measurement process and improve the overall quality of the measurement results.