# Rescaling oscilloscope signals and de-embedding cables

An oscilloscope measures the voltage that is applied to its input terminals. In most cases that works fine but, in some instances, it is necessary to move the measurement plane of reference and calibrate the oscilloscope’s measurements. For instance, if a minimum loss impedance pad (MLP) is used to terminate the measurement source in its expected impedance like 75 Ω instead of the 50 Ω oscilloscope input, then the measurement should be made relative to the impedance pad’s input. Likewise, if a transducer is used to measure a physical source, then measuring at the transducer input is required and the units of measurement might have to be changed. These are just a couple of instances where the oscilloscope measurements must be rescaled to change the plane of reference and possibly the units of measurement. There are also instances when the effects of connecting cables have to be removed so that the oscilloscope is looking at the cable input. This article will cover rescaling and de-embedding and provide some common examples of their usefulness.

Recalibrating for a 75 Ω input example

Consider measuring a signal from a 75 Ω source like a video camera. The camera is designed to work into a 75 Ω load. In order to ensure a proper impedance match between the source and the oscilloscope, a 75-to-50 Ω impedance pad is used to match the camera to the oscilloscope and vice versa. An L-Pad network is a common type of MLP. The impedance pad has a 75 Ω impedance for a signal attached to inputs.  It also has a 50 Ω impedance when looking into its output back towards the signal source. Figure 1 shows such a 75-to-50 Ω MLP.

Figure 1 An example of an L-pad impedance matching pad used to connect a 75 Ω source to the 50 Ω input of an oscilloscope. Source: Arthur Pini

Applying some basic circuit analysis, it is easy to see that this L-pad has an insertion voltage loss of 7.48 dB (gain of 0.422) when looking from the 75 Ω source to the oscilloscope. If the oscilloscope is used in its default mode, all the voltage measurements referenced to the 50 Ω output of the MLP would be 7.48 dB low. The oscilloscope has a couple of tools to rescale the input measurements to move the plane of measurement to the input side of the MLP.

The easiest to use is the input channel rescale function. On the oscilloscope in the following example (Figure 2), the rescale function appears in the channel setup dialog box.

Figure 2 The rescale function in the channel dialog box allow users to multiply the channel input by a constant, add or subtract a constant, and to change the units of measure. Source: Arthur Pini

The MLP has a gain of 0.422. Rescale is used to multiply the input signal by the reciprocal gain of 2.37 which will bring the signal level back to full scale at the MLP input. Measurements are now referenced to the input of the MLP and all the oscilloscope’s measurements, including cursor readouts and parameters, will read the voltages at that point. The video camera now works into a 75 Ω load and the oscilloscope sees a 50 Ω source impedance—all is well in the world.

The rescale function can also be used to convert the units of measure. This allows readings from sensors or transducers not only to be scaled correctly, but also to be measured in the appropriate physical units.

Accelerometer measurement example

The rescale function in this oscilloscope is also available as a math function that can be applied to an input channel or other types of oscilloscope traces. Using the math function allows you to see both the input and output waveform. Figure 3 shows the basic rescale operation including the unit conversion functionality.

Figure 3 The math rescale function provides the same basic operations as the channel rescale, but it allows users to see both the input and output waveform. Source: Arthur Pini

The signal source in this example is an accelerometer with a sensitivity of 10mV per g. The accelerometer is mounted on a small air compressor, monitoring vertical acceleration. The upper trace shows the accelerometer output which has vertical units of volts. Although the accelerometer sensitivity is given as mV/g, the rescale constant for reading in mV/m/s2 is used to facilitate the integration of acceleration to obtain velocity and displacement measurements in m/s and m respectively. The rescale function scales the voltage signal from the accelerometer by multiplying it by the reciprocal of the sensitivity in units of m/s2 per volt, a value of 980 E-6. The “override units” box is checked and the desired output units of m/s2 are entered into the “output units” box.

Viewing both the input and output of the rescale function permits user too study the characteristics of the input, like offsets, overloads, and issues like clipping that may affect the rescale results.

With the measurements units after the rescale operation changed to m/s2, it is possible to integrate acceleration into velocity and velocity into displacement as shown in Figure 4.

Figure 4 The flexibility to rescale units allows for the additional processing of the accelerometer signal with meaningful units of measure. Source: Arthur Pini

Each of the integration operations has a provision for adjusting gain and offset to eliminate accumulation errors caused by offsets.

The oscilloscope used in this example automatically changes the input units at each stage of the processing, so after the first integration the velocity trace is seen in units of m/s. After the second integration, the waveform is that of displacement measured in meters. The peak-to-peak value of the displacement is 9.13 nm. The fundamental frequency is 53.8 Hz which is related to the induction motor driving the compressor. As one can see, the ability to rescale amplitude and change units of measure is extremely useful.

The input channel rescale function can only be applied to the channel it is associated with. As mentioned previously, the math rescale function can be applied to other oscilloscope functions. So, if you want to scale the FFT of a signal from the native decibels relative to one milliwatt (dBm) to decibels relative to one volt (dBv), that requires subtracting 13 dB from the dBm reading. Using the math rescale function on the FFT output, the multiplicative constant is left as 1 and -13 is entered into the constant field. The units should be changed to dBv. This rescales the FFT to show the frequency spectrum with vertical units of dBv.

De-embedding functions example

De-embedding, though related to rescaling, is a more complex process. Rescaling simply allows a waveform to be multiplied by a constant and applying an additive constant. De-embedding is a process of correcting or removing frequency dependent variations in the signal. Basic de-embedding is available in some mid- and high-bandwidth oscilloscopes. The most basic form is cable de-embedding in the input channel, it is used to remove the effects on an interconnecting cable from a measurement. Like rescaling, this will move the measurement plane from the output of a cable to its input.

Cables act like low pass filters, limiting the bandwidth of a signal. Like low pass filters they reduce a signal’s amplitude by eliminating high frequency components. This also increases the risetime of pulse-like signals. The basic concept of de-embedding is that a de-embedding filter with a frequency response opposite of the cable’s frequency response is applied to the cable signal. The cable has a low pass response so the de-embedding filter should have a high pass response. The combination restores the original (cable-less) response as shown in Figure 5.

Figure 5 The basic concept of de-embedding is to counter the effect of the cable by filtering the cable output with a filter that has a complementary response, resulting in a flat spectral response. Source: Arthur Pini

The user interface for the cable de-embedding feature requires a description of the cable including its length, propagation velocity, and frequency response. The frequency response can be entered either as the S21 s-parameter forward transfer function as a table or as attenuation per 100 feet as a function of frequency by supplying the constants A1 and A2 from the manufacturer’s frequency response equation. That equation is in the form of:

A1 *√ frequency+A2*frequency.

The two terms in the equation represent the resistive losses and the dielectric losses.

An example of cable de-embedding on a 1.25GS/s NRZ waveform connected via a 1-meter RG316 cable is shown in Figure 6.

Figure 6 The cable de-embedding setup using the attenuation equation for a 1-meter RG316 cable with an insert (in the red box) showing the signal before de-embedding. Source: Arthur Pini

The red box contains a view of the signal before de-embedding. It has a mean rise time of 236 ps, fall time of 236ps, and an amplitude (top to base) of 300.3 mV. The de-embedding setup uses the insertion loss equation with manufacturer’s supplied constants (A1=25.393, and A2= 3.017), a length of 1 meter, and a velocity factor of 0.66. The de-embedding has reduced the mean rise time by 6 ps, the mean fall time by 6.4 ps and increased the mean amplitude by 10.8mV. Cable de-embedding has improved the quality of the signal by reducing the cable effects.

This cable de-embedding function is standard on this oscilloscope. Most manufacturers of high-performance oscilloscopes offer a more complete de-embedding software option intended for serial data stream compliance testing with capabilities of de-embedding cables, motherboards, and fixtures. They enable virtual probing anywhere in a device under test.

The utility of rescaling and de-embedding

Rescaling and de-embedding are very useful features for designers and test engineers to be aware of. They are needed to handle input interface issues that might otherwise lead to serious measurement errors.

Arthur Pini is a technical support specialist and electrical engineer with over 50 years of experience in electronics test and measurement.

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