How to read sensors with a scope
Certain functions of oscilloscopes let you scale voltage inputs into engineering
units.
By Arthur Pini
Electronic Measurement and Analysis Consultant
Oscilloscopes mainly measure voltage and time. Measuring another physical property such as temperature,
pressure, flow, velocity, or displacement on an oscilloscope requires use of a transducer or sensor to convert
the measured quantity into voltage. Using the oscilloscope's rescale function you can scale the input voltages
into units that match the transducer's input.
Some oscilloscopes handle the rescale operation by changing the probe gain in the channel input menus. This
provides numerically correct values but does not generally change the units of measure. The math function,
rescale, lets you multiply the acquired waveform samples by a constant, add a constant (mx+b), and also
modify the readout units.
Let's take an example of a third-party current probe. The current probe's manufacturer specifies the probe's
sensitivity of 0.33mV/mA when operating into 50Ω. To read the oscilloscope measurements in milliamperes,
you need to multiply the measured values by 3mA/mV, the reciprocal of the current probe's sensitivity. Figure 1
shows an example of using an oscilloscope’s rescale function to convert the vertical scale units from mV to mA.
Figure 1: An oscilloscope's rescale math function produces a display of the output of a current probe
directly in milliamps. The voltage values are multiplied by a factor of 3mA/mV (the reciprocal of the
probe's 0.33mV/mA published sensitivity, which changes units from Volts (top trace) to Amperes
(bottom trace).
The current probe output is applied to channel 1, where we see the rms amplitude, shown in parameter P1, is
10.6 mV. The rescale math function is setup in math trace F1. Rescale offers the ability to multiply a signal by a
constant and add a second constant as shown in the rescale dialogue box in the lower right. In figure 1, the
readings from channel 1 are multiplied by 3. Rescale also has the capability to override the units and select
other common units of measure. In this case the units are changed to Amperes (A). Parameter P2 reads the
rms current applied to channel 1 as 31.8mA. Cursors or other parameters applied to math trace F1 will also
read correctly in Amperes.
The second example takes the output of an instrument microphone and reads the sound pressure level (SPL) in
units of pressure (Pascals or Pa). In this example we will employ a SPL calibrator to determine the sensitivity of
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the microphone. Figure 2 shows the use of the rescale function to read the microphone outputs directly in
Pascals.
Figure 2: Rescaling the oscilloscope vertical axis to read a microphone output directly in units of
sound pressure level. Channel 1 is the microphone input and math trace F1 is the same signals
rescaled to read in Pascals.
Figure 3: Starting with the output of an accelerometer, readings of acceleration in g's (F1), velocity in
inches per second (F2), and displacement in inches (F3) is accomplished using repeated application
of integration and rescaling.
The microphone is inserted into a SPL calibrator, which supplies an acoustic signal of 110dB rms relative to
20µPa at 1kHz. The output of the microphone is connected to channel 1. The rms voltage, read by parameter
P1, is 265.8mV. The first step in the calibration is to convert the calibration level into Pascals. The calibrated
110dB rms relative to 20µPa level works out to 6.32 Pa. The sensitivity of the microphone is computed as
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6.32/0.2658 or 23.78Pa/V. This is entered into the multiplier field in the rescale math function. The Override
units box is checked and the output units are specified as PAL for Pascals. The rms value of math trace F1 now
reads the expected value of 6.32Pa.
Scaling to engineering units
Math functions in these oscilloscopes can be chained, which lets you perform multiple conversions. For
example, you can take the output from an accelerometer and read out acceleration, in gs, and then rescale and
integrate the waveform to read the velocity in inches per second (ips). The velocity can be then integrated to
read the displacement in inches. Rescaling can also be applied to parameters using parameter math so peak to
peak measurements can be converted to peak. Figure 3 shows the final result.
The signal from the accelerometer is applied to channel 1. Parameter P1 reads the peak-to-peak value of 20.1
mV. The accelerometer has a sensitivity of 9.9mV/g. The first rescale operation in math trace F1 scales the
data by the reciprocal of the accelerometer sensitivity, 101g/V. The output of trace F1 is now calibrated to read
in g. Parameter P3 reads the peak to peak acceleration as 2g. In P4, the peak to peak acceleration is divided
by two and reads the peak acceleration of nominally 1g.
In math trace F2, we rescale and integrate the waveform from F1. The math functionality of this oscilloscope
supports two math operations per trace and allows rescaling and integration to convert from acceleration in gs
to velocity in ips. The rescale multiplier is 386.08 which converts gs into inches/s² the units are changed to
reflect this. After rescaling the signal is integrated and the units are automatically changed to ips. Parameter P5
(peak to peak velocity in ips) is divided by 2 using parameter math in P6 to read the peak velocity as 0.621ips.
The final step is to integrate the velocity (done in math trace F3) to obtain the displacement which is read using
parameter P7 as 0.002inches (min – milliinches) peak to peak.
Oscilloscopes equipped with a rescale capability can read out waveforms and measurements correctly scaled
and in the proper units Regardless of the sensor. This process can be chained through multiple operations,
each requiring its own rescaling and mathematical operation. About the author
Arthur Pini is an electronic measurement and analysis consultant with over 50 years experience in the test and
measurement industry. He has an extensive knowledge of oscilloscope, real-time spectrum analyser, frequency
synthesisers, and arbitrary function generator measurements and applications.
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