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# System prepended metadata

title: '[Oscilloscope] Probe Compensation'
tags: [Electronics, Oscilloscope]

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title: 
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###### tags:  A Journey Through Electronics

# Probe Compensation
This article explains how to properly compensate an oscilloscope probe for accurate measurements.
## 1. The probe 
:::info
This is a short intro for those not familiar with oscilliscope probe. If you already know, please jump to [next](#section2).
:::


A standard oscilloscope probe is a passive cable with a BNC connector and a tip. When using it, you plug it into a oscilliscope and use the tip to measure the signal. Most passive probes(Fig.1 & Fig.2) feature a switch to select between two attenuation settings: 1x (no attenuation) and 10x (attenuating the signal by a factor of ten). For example, a 5V signal would be displayed as 5V in the 1x setting and 0.5V in the 10x setting. 

This attenuation function, while useful, is where problems can arise.

<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/Hy699hn_xx.png"style="width:50%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.1 Passive Probe
    </figcaption>
</div>

([Image Source](https://electricalacademia.com/electronics/oscilloscope-work-oscilloscope-parts-functions/))

<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/Sylmdn3Ogl.png"style="width:50%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.2 Passive Probe
    </figcaption>
</div>

 ([Image Source](https://www.rohde-schwarz.com/se/products/test-and-measurement/essentials-test-equipment/digital-oscilloscopes/oscilloscope-probe-tips-and-how-to-use-them_257202.html#gallery-5))

<a id="section2"></a>
## 2. Circuit
:::info
What would be the problem?
:::

Let's take a look at a simplified probing circuit in Fig.3. 

The $R_{scope}$ and $C_{stray}$ are the impedance and stray capacitance inside a scope. Usually, you can find the impedance of a scope easily in its datasheet.

<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/ByPzDk6ugl.png"style="width:70%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.3 Oscilloscope circuit
    </figcaption>
</div>

As mentioned in previous paragraph, a probe can measure a signal witouht or with attenuation. 

### Without Attenuation ($\times 1$)
When no attenuation selected, the impedance is relatively low compared to scope's internal impedance, making $V_{Source} \approx V_{Scope}$. 

In addition, the stray capacitance and resistance of the probe cable would act like a low-pass filter, make a no-attenuation probe suitable for measuring low-frequency signals (Low bandwidth in other word).

<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/r1EBWKyFlg.png"style="width:70%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.4 "x1" probing circuit
    </figcaption>
</div>

### With Attenuation ($\times 10$)
:::info
The problem shows up
:::
Now, we need it to attenuate a signal 10 times smaller, intuitively, we will put a $9 M \Omega$ resistor in series to form a voltage dividor of $\frac{1}{10}$ voltage output ($V_{Scope} = \frac{1}{10} V_{Source}$).

<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/Bk8JVK1Kle.png"style="width:70%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.5 "x10" probing circuit
    </figcaption>
</div>

Sounds fair, doesn't it?

It is true for DC signal, but when the frequency get higher, the stray capacitance ($C_{Stray}$) start to mess up. Recall the formula of capacitor's impedance:

$$Z_{c}=\frac{1}{j \omega C}$$

The impedance of the stray capacitor is decreasing when freuency goes up, which makes the voltage dividor, ==not $\frac{1}{10}$ anymore==. 

For an ideal oscilloscope, it should keep the same level of attenuation across its supported bandwidth, which is not fulfilled with this setup.

## 3. Compensation 

### Frequency Response
To prove what I mentioned, simulation is a good way to examine it. 

From Fig. 6, it is the frequency response for "$\times 10$" probe with resistance only. It supposes to be -20dB across all frequency according what we expect a probe should be, but it is not. 

<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/rkJ7K-zFxg.png"style="width:90%; height:auto;" />
    <img src="https://hackmd.io/_uploads/HyNZKbzteg.png"style="width:90%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.6 Resistance only
    </figcaption>
</div>


To solve this, we use a trick of adding a capacitor(C1) in parallel with the resistor(R2). This creates a second voltage divider, and make it possible to have **same attenuation level across all frequency**. However, viewing frequency response in Fig.7 and Fig.8, it is still not perfect. 

<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/SkuykPmKeg.png"style="width:90%; height:auto;" />
    <img src="https://hackmd.io/_uploads/BJlCAU7tge.png"style="width:90%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.7 C1 is smaller than perfect value
    </figcaption>
</div>

<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/ryh8ovQKlg.png"style="width:90%; height:auto;" />
    <img src="https://hackmd.io/_uploads/HkCrjwQtge.png"style="width:90%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.8 C1 is larger than perfect value
    </figcaption>
</div>

:::info
The perfect value is achieved when the resistive voltage divider's ratio matches the capacitive voltage divider's ratio across all frequencies.

However, the perfect value, usually, is not possible to find among off-the-shelf capacitors.
:::

### Add the Compensation Capacitor
Now we add one more capacitor (C3), which can be adjusted. This is the ==compensation capacitor==. It adjusts the impedance by a screw either near the probe's BNC connector (or probe tip). Fig.9 is the response with perfectly tuned capacitance value, a straight line on the chart.  



<div style="text-align:center">
    <img src="https://hackmd.io/_uploads/ryrjNp4tle.png"style="width:90%; height:auto;" />
    <img src="https://hackmd.io/_uploads/HJE3ET4tex.png"style="width:90%; height:auto;" />
    <figcaption style="font-size:14px; ">
      Fig.9 Perfect capacitance value
    </figcaption>
</div>


## 4. Summary
A standard 10x probe uses a resistive voltage divider, which works for DC signals but fails at higher frequencies because of the oscilloscope's stray capacitance. It distorts the signal, causing inaccurate readings and a non-flat frequency response. 

To solve this, a small, adjustable compensation capacitor is added to the probe's circuit. By adjusting this capacitor, you can balance the resistive and capacitive dividers, ensuring the probe provides a consistent 10x attenuation across its entire bandwidth.

## Reference
1. https://www.allaboutcircuits.com/technical-articles/an-introduction-to-oscilloscope-probes/
2. https://www.rohde-schwarz.com/se/products/test-and-measurement/essentials-test-equipment/digital-oscilloscopes/oscilloscope-probe-tips-and-how-to-use-them_257202.html#gallery-5
3.  Hayes, Thomas C., David Abrams, and Paul Horowitz. Learning the Art of Electronics: A Hands-On Lab Course. Cambridge University Press, 2025