How to design an oscilloscope passive probe (part II)

Abstract

Following the previous post  how to design passive oscilloscope probe (part I) , In this paper we will study from the theoretical point of view, the basic principle of a passive oscilloscope probe, calculate its input impedance,  tips to use, and finally establish the basis for DIY homemade 10:1  passive probe.

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5. HOW WORKS AN OSCILLOSCOPE PASSIVE PROBE ?

The passive probe is the most known and used of al general all purpose probes. As the name says, "passive" suggests that it is made of passive components such as resistors, cables, capacitors, and indeed it is.

In Part I of this article, we have seen how the oscilloscope impedance and cables capacitance affect to the measure up to the point of being able to make it unrecognisable (it was an uncompensated probe). Given that the basic principle of any measuring equipment is to measure the signal without distorting it, we will raise the theoretical equations governing the operation of a passive probe compensation that allow us to maintain the signal integrity during the measurement. 

 The purpose of this section is to analyse from the theoretical point of view the most basic oscilloscope passive probe. The proposed scheme is valid for general purpose medium/low oscilloscope probes. For high-end passive probes, the scheme is a bit more complicated due to there are more components inside for low and high frequency compensation doing the theoretical explanation a little more confusing leaving out of the scope of this article. 

As a starting point for the mathematical approach, we assume that the probe cable is sufficiently short compared with the wavelength of the signal to be measured. This hypothesis will also greatly facilitate us the analysis in most cases. In this way, we will only consider the coaxial cable capacitance as  a "short line" and we will not consider the mathematical model of the cable as a transmission line.

As we have seen in the first part, if we add a piece of coaxial cable to the oscilloscope input, forms a low pass filter that depends on the impedance measured. Fortunately, compensate the influence of that pole is relatively easy. Just remembering a little of mathematics we learned during the studies and adding a zero in the measurement circuit using the components Rp (9 MOhm) and Cp (variable) (see Figure 1).

Figure 1 - Oscilloscope passive probe Schematic 

Let be Ct the total cable capacity over the oscilloscope input

Ct= Cs+ Cc

Figure 2 - Equivalent circuit

And the relationship between the input and the output of the probe

Z1= Rp1 + Cp⋅ Rp⋅ S    ( 1 )

with

Z1= Rp/ / Cp    ( 2 )

Z2= Ct/ / Rs    ( 3 )

Developing terms the impedances Z1 and Z2 are obtained as

Z1= Rp1 + Cp⋅ Rp⋅ S    ( 4 )

Z2= Rs1 + Ct⋅ Rs⋅ S    ( 5 )

Replacing the equations (4), (5) in (1) and simplifying, we obtain the probe transfer function:

UsUe= Rs( 1 + CpRpS)Rp( 1 + CtRsS) + Rs( 1 + CpRpS)    ( 6 )

The transfer function shows there are a zero and a pole, in principle without relation between them, but if we can enforce the relationship (7), we can simplify the transfer function (8)

Cp⋅ Rp= Ct⋅ Rs    ( 7 )

UsUe= RsRs+ Rp= 110    ( 8 )

Therefore, in order to fulfill the attenuation ratio 10:1 is mandatory that the adjustable capacity meets the equation (7). Clearing Cp from (7) we obtain the condition to be fulfilled by the trimmer capacitor.

Cp= ( RsRp) Ct    ( 9 )

6. WHEN USING THE ATTENUATION X10?

X10 probe attenuation will be used when:

1. We want to enjoy the full bandwidth of the oscilloscope without limitations. In General, we can say that the bandwidth is limited by the component that has lower bandwidth (probe or oscilloscope).
2. The circuit impedance is near to the impedance of the oscilloscope . In this case, the insertion of the probe causes the formation of a resistive divider between the Thevenin equivalent impedance of the circuit and the oscilloscope input impedance reducing the signal level. The signal showed in the oscilloscope is not displayed as it is. Also, we may have problems due to excessive current drain from the signal.
3. The signal to measure includes high frequency components or abrupt edges that have to be accurately measured . In the previous post we have seen how the fact of measuring a signal without a suitable probe reduces the bandwidth of the oscilloscope. In order to measure accurately rise/fall times, we have to ensure a bandwidth of at least
   B W= 0.35tr    ( 10 )
   tr= s i gn a l  r i s e  t i m e
4. The oscilloscope input capacitance affects the circuit under test. Oscilloscope probe parallel coupling with poorly compensated probe can cause that resonant circuits as used in RF, modified their operation. For example the RF oscillator frequency could change simply by the fact of measuring its signal.
5. The signal voltage exceeds the oscilloscope input range. The range of the input stage of an oscilloscope is limited to a few volts . If we have to measure higher voltages, coupling X10 means we could measure signals 10 times larger than the oscilloscope input range.

For the following cases, if desired, it is not necessary to use the x10 oscilloscope probe option. Instead of it may alternatively use "wire" or other connection when:

1. We do not mind sacrificing the bandwidth of the oscilloscope.
2. The circuit impedance to measure is much smaller than the input impedance of the oscilloscope. In this case, the coupling impedance of the oscilloscope to the circuit being measured causes a slight distortion in the measured signal that will be smaller the lower the impedance of the circuit being measured and in many cases negligible.
3. The signal frequency components are low or it is not interesting measuring the signal edges accurately.

7. HOW AFFECTS THE INSERTION PROBE TO THE MEASURE?

As mentioned, the simple act of measuring, alters the original signal. Our purpose will be change as less as  possible the circuit under test.

All Previous analysis was from oscilloscope  point of view. We wanted to know how the oscilloscope sees the signal sensed by the probe. But now, we must ask ourselves the following question. From the point of view of the signal, how the measuring equipment is seen? . Among the factors to consider when connecting the oscilloscope probe to the circuit under test, we have:

• The parasitic capacitance due to "ground wire" and probe. "This impedance is in the order of a few pF and it will not be considered in this analysis.
• The equivalent impedance formed by the probe and "seen" by the signal . In this case will be Z1 + Z2.

For analysis, we will calculate the input impedance showed by the oscilloscope and the probe.

Figure 3 - Oscilloscope plus probe input impedance 

The signal "sees" the probe as an impedance:

Ze n t= Z1+ Z2    ( 11 )

Considering equations (2) and (3) we can write

Ze n t= Rp( 1 + CpRpS)+ Rs( 1 + CtRsS)    ( 12 )

And if clearing the condition (7), the input impedance can be expressed as

Ze n t= Rp+ Rs( 1 + CtRsS)    ( 13 )

The impedance (13) corresponding to the oscilloscope and probe is connected in parallel with the signal to be measured, thereby altering the circuit. Depending on the output impedance of the signal, the fact connect the probe may cause the measure to be invalid . The lower the output impedance of the signal, the better the measure.

From equation (13) follows:

• At low frequencies, the impedance will be about 10 MOhms.
  Ze n t= Rp+ Rs= 10 MΩ  ;  Si  1 > > CtRsS    ( 14 )

• At high frequency, the impedance is:
  Ze n t= Rp+ RsCtRsS     ;  Si  CtRsS> > 1     ( 15 )

Analyzing in frequency the impedance who the signal "sees" (Zent), we have a pole that will cause a drop of 20 dB / decade in

fp ole    ( Ze n t) = 12 πCtRs    ( 16 )

In general, one decade below the cutoff frequency have an impedance of 10 MOhm and one decade above the cutoff frequency will fall to 20 dB / dec.

Note how the input impedance varies with frequency starting from 10 MOhms and decreasing to negligible limits. If we perform a little calculation with 1.5 meters of coaxial cable (50 Ohm RG-316, capacity 96 pF / m) gives a cutoff frequency of 1460 Hz

fp ole( Ze n t) = 12 π⋅ ( 96 + 13 ) p F⋅ 1 MΩ       = 1460  Hz ! ! !     ( 17 )

In this particular case, it means that in frequencies below than 1.4 kHz the input impedance will be approximately 10 MOhm and in higher frequencies begins to decay in the order of 20 dB per decade.

For reference, next figure shows the Tektronix P2220 probe input impedance versus frequency and how the cut-off frequency is around 1.5 KHz (Figure 5, at the intersection with 45 º).

Figure 4 - Probe Tektronix P2220 Input impedance 

Next figure shows phase change versus frequency and we can see clearly the pole influence dephasing 90 ° at high frequency.

Figure 5 - Phase versus frequency Tektronix P2220 probe

8. PRACTICAL EXAMPLE OF DESIGN OF A PROBE OSCILLOSCOPE

In this section we will implement all the theoretical part shown above. To do this, we will design a home oscilloscope 10:1 ratio probe where we will see the influence of the adjust capacitor. As I had not a variable capacitor, I took several fixed-value capacitors in parallel, so that I can be adding capacity by coupling the circuit according to the following drawing:

Fig.6-homemade oscilloscope probe setup

8.1 MATERIAL REQUIRED

• Coaxial cable RG-316, length 1.20 m.
• SMD capacitor values ​​2.7 pF, 6.8 pF, 10 pF and 22 pF.
• SMD resistor value of 9 MOhm.
• Oscilloscope Tektronix TDS3000 or similar.

8.2 SETUP

To perform the test, I used the square wave output generator from the oscilloscope that is used to compensate probes.

•  TEST 1:  We take as reference the oscilloscope's commercial probe properly compensated. We see that the displayed waveform is completely square and that will be our goal to achieve.

Fig.7-Passive probe compensated

• TEST 2: Using the DIY assembly without adding  any capacity. All switches are open.

Fig.8-Probe with 0 pF compensation

• TEST 3: DIY assembly adding 2.7 pF.

Fig.9-probe with 2.7 pF compensation

• TEST 4: DIY assembly, adding 6.8 pF.

Fig.10-probe with 6.8 pF compensation

• TEST 5: DIY assembly adding 10 pF.

Fig.11-Probe with 10 pF compensation

• TEST 6: DIY assembly adding 22 pF. Here we can see how we have passed compensating the probe. The optimum value is between 10 pF and 22 pF.

Fig.12-Probe with 22 pF compensation

• TEST 7: DIY adding 12 pF (10 pF / / 2.7 pF). For this value we should be near to the optimum compensation. 

Fig.13-Probe with 12 pF compensation

Due to we do not have a variable capacitor, the setup showed in test 7, is the best we can get. Note also that if we calculated theoretically the value we need (Equation 7), we obtain a value around 14 pF . This value is very close to the final one. 

9. PART II. CONCLUSIONS

1. Maximizing bandwidth by adjusting the probe. To maintain as maximum as possible the bandwidth, adjust the variable capacity of the probe to compensate the oscilloscope's pole.
2. Avoid the exchange of probes between oscilloscopes. A probe adjusted for one oscilloscope may not be right for another one, since each has its own oscilloscope input impedance.
3. Probe bandwidth. When we have to buy an oscilloscope probe, we must ensure that the bandwidth is sufficient for the oscilloscope we have. The probe chosen affect the overall bandwidth.
4. If you are going to measure high frequency signals , the proposed mathematical analysis begins to be compromised together to the feasibility of passive probe. In this type of signals, it is better to consider RF probes based on FET also called active probes.
5. If we chose to design our own probe , you have to pay special attention to the selection of components. The capacitors will be searched to have flat response versus frequency and the resistors will have low inductive components in the whole bandwidth .
6. When connecting the probe to the circuit under test, we are adding an impedance in parallel , depending on the output impedance of the signal, this extra load could affect to the measurement dramatically.