Within self-designed 50Ω probes, the effects of transmission lines on measurements need to be considered because every connection creates impedance discontinuities.
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In hard-switched applications (i.e. non-resonant-transition switching) where the semiconductor switch determines the dV/dt on its drain, the switching speeds are typically less than 10nsec. This can produce voltage and current spikes within the circuit with edges equal to or higher than those from the power switch.
Within self-designed 50Ω probes, you must consider the effects of transmission lines on your measurements. Every connection, whether a connector connection or a solder connection, creates impedance discontinuities within the transmission-line model. This creates points of signal edge reflection for the high frequency components of the signal (edges). Figure 6 shows a representative transition line model.
Figure 6: For an n:1 voltage probe, you need a transmission-line equivalent model.
The performance of the n:1 50Ω voltage probe is much more complicated than that of just two resistors. The high-frequency components of the signal see the reactive elements within the transmission-line model and are amplified and reflected by its elements.
The shield essentially forms a Faraday cylinder around the centre conductor where no external EM field penetrates. In Fig. 6, the lengths of the unshielded leads at the target source are susceptible to EM noise energy (NS) and are not part of the "real" signal. This noise adds to the real signal and can only be reduced by reducing the length on the sense leads (and any additional PCB trace lengths).
Once the signal enters the coaxial cable, the situation becomes a transmission-line issue. Here, the signal travels through the cable at approximately 0.67 times the speed of light. When the signal encounters an impedance discontinuity such as a connector, a portion of the signal reflects back to the source. The reflected signal is also summed into the input signal. It appears as an inverted edge and at two times the one-direction travel delay. Now the question is "What part of the signal is real and what part is summed-in transmission line effects?"
To reduce the transmission line effect, you can dampen the cable constituents. This is called compensation, typically done by adding a series RC network across the BNC connector signal-to-ground connections (as also seen in Fig. 6). Its intent is to nullify the reactive impedance presented by the coax cable. This will reduce the parasitically induced signal being summed into the real signal. Unfortunately, nothing comes without a price, for it will reduce the probe's bandwidth. By how much is a matter of the operator's aesthetic preferences. Figure 7a shows an oscilloscope plot of an uncompensated 1,000:1 50Ω voltage probe on the drain of a high-performance superjunction MOSFET within a PFC converter. Figure 7b shows the waveform from a compensated probe.
Figure 7a: Oscilloscope Plots of a 1000:1 50Ω voltage probe without compensation show ringing.
Figure 7b: Compensation with a 10Ω resistor and 470pF capacitor reduces ringing.
When we compare the relative rise time and fall time of the drain signals (Figure 8a), you can see a slight reduction in the switching speeds (Figure 8b).
Figure 8a: Uncompensated 1000:1 50Ω voltage probe shows ringing, edge delay, and reflections.
Figure 8b: A compensated probe with 10Ω resistor and 470pF capacitor shows a cleaner waveform.
In Fig. 8a, the leading-edge spike and the ringing is horrendous, but it is the most accurate view of the turn-off voltage risetime (tRV). It also shows evidence of a reflection, just behind the leading-edge spike. Figure 8b is the same probe with compensation. The waveform is more aesthetically acceptable. It attenuates the ringing, but also slows the risetime (it is still better than the commercially available probe). Therefore, you should use the uncompensated probe for all rise and fall time (dV/dt) measurements and the compensated probe for all other power supply observations.
You can try to assign values for compensating compenents R and C by attempting to model the probe system. This means trying to define the undefinable. Eventually, you just have to sit at the bench and manually adjust the final values to a qualitative "optimum" solution. Such work can be tedious, especially when working with small PCBs and surface-mount parts that you must be manually unsolder and solder into the PCB with every circuit change.
There are a number of R and C value combinations that result in similar results. Some tips and observations from more experienced engineers may help you along the way.
Figure 9: Compensating a probe with an RC circuit will dampen the output.
From my experience, the optimum resistor value range seems to be from 10Ω to 47Ω. Values above this range appear to increase the amplitude of the resonant spikes on the signal. The industry appears to use a capacitance value of around 470pF. This is a good starting point. With the compensating resistor installed, try a capacitance value below and above this value. You want to determine the minimum value of capacitance that will yield the desired results. Higher values of capacitance will slow the rise and fall times and the peak amplitudes of the real signal. Capacitance values of between 470pF to 680pF appear to result in a reasonable compensated wave shape.
Marty Brown is presently an electronic engineering consultant in the area of efficient electronic power conversion and power semiconductor definition.
First published by EDN.