Introduction

The Rescale function, available both as a math function and a parameter math function, lets you multiply the amplitude of an acquired waveform by a constant or multiply by a constant and add a constant. Additionally, the units of measure for the rescaled function can be converted to a wide variety of common units.

This function is used with special sensors or probes to obtain calibrated amplitude readouts in the units that match the sensor readings. It can also be used to switch between one system of units and another.

In the following tutorial you will use the rescale math function to convert a voltage reading to a current reading, remove a bias offset, and scale measurements

Equipment Required

WaveRunner 6 Zi Oscilloscope
Passive probe

Initial Setup

Displays shown in the tutorial are based on the following initial setup on a WaveRunner 6 Zi oscilloscope:

  1. Connect a passive probe from Channel 1 to the CAL test point on the front panel. The CAL output is a 1 kHz square wave with an amplitude of 1 V
  2. Recall the default setup by choosing: File > Recall Setup > Recall Default.
  3. Turn off Channel 2.
  4. Auto Setup the scope: Press Scope Setup on the front panel. Select Auto Setup from the flyout menu.
  5. Using the C1 dialog box, set the Channel 1 vertical scale to 200 mV/division and the vertical offset so that the bottom of the trace is one and one half divisions above the bottom of the display grid.
  6. Set the trigger level to 500 mV.
  7. This completes the initial setup. The scope display should be similar to Figure 1.

Figure 1:

The scope display after performing the steps of the initial setup

Using the Rescale Function

We will rescale the waveform on Channel 1 to read the current into the probe tip. This is done by dividing the voltage waveform by the probe input resistance of 10 MOhms using the rescale math function.

Open the Math dialog box by choosing: Math> Math Setup>.

Select the F1 tab on the Math dialog box.

Select the source as Channel 1, the operator as rescale. Touch or click the Trace On box to display F1.

Touch or click on the Rescale tab on the right side of the math dialog.

Double touch or click on the First Multiply By box. When the pop-up keypad appears, enter the number 100Exp -9 and press OK. This will cause all the samples in the Channel 1 waveform to be multiplied by 1e-7 (the same as dividing by 10 MOhms).

Click or touch the Override Unit check box, a check mark will appear along with an Output Units box. Touch or click on the output unit’s box. An onscreen keyboard will appear. Type in the units as A for Amperes, then, press OK. The units in the F1 trace annotation box should change to nA.

The screen should appear as shown in Figure 2.

Figure 2:

The setup for the rescale math function converting the voltage reading of Channel 1 into current drawn by the probe

Supported Output Units abbreviations are as follows:

1. (blank) - No units21. L - Liter41. T - Tesla
2. A - Ampere22. M - Meter42. UI - Unit interval
3. C - Coulomb23. FT - Foot 43. V - Volt
4. CYCLE - Cycles24. IN - Inch 44. VA - Volt amps
5. DB - Decibel 25. YARD - Yard 45. W - Watt
6. DBC - Decibel referred to carrier26. MILE - Mile 46. WB - Weber
7. DBM - Decibel Milliwatt 27. N - Newton 47. MIN - Min
8. DBV - Decibel Volts 28. OHM - Ohm 48. HOUR - Hour
9. DBUZ - Decibel Microamp 29. PAL - Pascal49. DAY - Day
10. DEC - Decade30. PCT - Percent50. WEEK - Week
11. DIV - Divisions 31. POISE - Poise
12. Event - Events32. PPM - Parts per million
13. F - Farad 33. RAD - Radian
14. G - Gram34. DEG - Degree (of arc)
15. H - Henry35. MNT - Minute (of arc)
16. HZ - Hertz36. SAMPLE - Sample
17. J - Joule37. SWEEP - Sweeps
18. K - Degree Kelvin38. SEC - Second (of arc)
19. CEL - Degree Celsius39. S - Second
20. FAR - Degree Fahrenheit40. SIE - Siemens

You can also enter combinations of the above units following the SI rules:

  • For the quotient of two units, use the character
  • For the product of two units, use the character
  • Exponents can be represented by a digit appended to the unit without a space

For example:

  • Acceleration can be entered as M/S2 for meters per second squared
  • Volts seconds can be entered as V.S

In some cases, the units entered may be converted to simple units. For example entering V.A will display W (watts).

Continuing With the Tutorial

Open the Math dialog box again.
Define the trace F2 to be the integral of F1. Turn on trace F2. The screen should appear as shown in Figure 3:

Figure 3:

Integrating the current waveform in trace F2 produces a ramp-like function due to the unipolar input signal

Because the trace F1 is unipolar positive the integral produces a ramp-like waveform as the positive mean value (as measured using the parameter P1) accumulates with time. If we want to see the integral of the waveform separate from the accumulating offset we need to remove the mean value. We can do this by subtracting the mean value of the waveform. Use the Then Add field of the rescale function to add a constant. In our case the constant is the value of the mean multiplied by -1 in order to subtract it from the integral operation.

Measure the mean of trace F1 using P1 as shown in Figure 3 by choosing Measure> Show Table>Statistics On >P1 Tab>Source F1>Measure Mean>.

Using the Math setup dialog, select tab F1, then on the Rescale tab enter -1 times the mean value of F1, as measured by P1, into the Then Add field.

Turn off the measurement parameters.

The waveform should now appear as shown in Figure 4.

Figure 4:

Using the rescale constant to remove the mean value of the waveform in Channel 1 before integrating

Note that the mean value of the F1 waveform is at zero and the integral no longer increases with increasing time. The integral function also incorporates a rescale operation, and we could have done the same thing there. We chose to use the rescale function because it also offered the ability to redefine the units of the measurement. Note that the trace annotation box for F2 now lists the units as C for Coulombs. So once units are redefined, subsequent math operations show the correct units of measure.

You can also rescale parameter measurement values by using Parameter math (optional) as shown in Figure 5.

Figure 5:

Using parameter math to rescale the amplitude measurement from Volts to Amperes

Turn off the F1 math trace.

Using the measurement setup dialog box, set up parameter P1 to measure the amplitude of C1.

Touch or click on the P2 tab

Select Math on Parameters.

Enter P1 as the source and P Rescale as the Math Operator as shown in Figure 5.

Enter the value 100 exp -9 into the First Multiply by field.

Change the units as we did in the rescale math function so that the parameter P2 reads out in Amperes (A).

The parameter P2 now reads the amplitude of the current flowing into the probe tip.

Conclusion

The rescale function in either math or math on parameters allows us to scale waveforms by multiplying by a constant, and multiplying by then adding a constant. You can also use these functions to change the units of a trace or parameter.

This completes the tutorial.