### Introduction

The Rescale function, a math function, lets you multiply the amplitude of an acquired waveform by a constant or multiply by a constant and then 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

WaveSurfer MXs-B Oscilloscope
Passive probe

### Initial Setup

Displays shown in the tutorial are based on the following initial setup on a WaveSurfer MXs-B 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 Auto Setup on the front panel. Select Confirm from the pop-up 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

1. 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.
2. Open the Math dialog box by choosing: Math > Math Setup > .
3. Select the source as Channel 1, the operator as rescale. Touch or click the Trace On box to display the trace.
4. Touch or click on the Rescale tab on the right side of the math dialog.
5. 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).
6. Click or touch the Override Unit check box, a check mark will appear along with an Output Units box.
7. Touch or click on the output units box. An onscreen keyboard will appear. Type in the units as A for Amperes, then, press OK. The units in the Math 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 units 21. L - Liter 41. T - Tesla 2. A - Ampere 22. M - Meter 42. UI - Unit interval 3. C - Coulomb 23. FT - Foot 43. V - Volt 4. CYCLE - Cycles 24. IN - Inch 44. VA - Volt amps 5. DB - Decibel 25. YARD - Yard 45. W - Watt 6. DBC - Decibel referred to carrier 26. 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 - Pascal 49. DAY - Day 10. DEC - Decade 30. PCT - Percent 50. WEEK - Week 11. DIV - Divisions 31. POISE - Poise 12. Event - Events 32. PPM - Parts per million 13. F - Farad 33. RAD - Radian 14. G - Gram 34. DEG - Degree (of arc) 15. H - Henry 35. MNT - Minute (of arc) 16. HZ - Hertz 36. SAMPLE - Sample 17. J - Joule 37. SWEEP - Sweeps 18. K - Degree Kelvin 38. SEC - Second (of arc) 19. CEL - Degree Celsius 39. S - Second 20. FAR - Degree Fahrenheit 40. 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

Save the Math trace to M1 (File pull down>Save Waveform>Save To Memory>Source Math>Destination M1>Save Now!).

Open the Math dialog box again. Define the Math trace to be the integral of M1. Turn on the Math trace.

The screen should appear as shown in Figure 3:

#### Figure 3:

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

Because the trace M1 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.

1. Turn off the M1 trace and open the Math trace dialog box. Select the source to be C1 and the Operator to be Rescale.
2. Touch or click on the Rescale tab on the right side of the Math dialog.
3. Double touch or click on the First Multiply By box. When the pop up keypad appears, enter the number 100Exp -9 and press OK.
4. Click or touch the Override Unit check box, a check mark will appear along with an Output Units box.
5. Touch or click on the output units box. An onscreen keyboard will appear. Type in the units as A for Amperes, then, press OK. The units in the Math trace annotation box should change to nA.
6. Measure the mean of the Math trace using P1 (Measure Pulldown>Measure SetupI>Show Table checked> Statistics On >P1 >Source Math>Measure Mean>).
7. Using the Rescale tab in the Math setup dialog enter -1 times the mean value of the Math trace, as measured by P1, into the Then Add field. Save this waveform as M2 (File pull down>Save Waveform>Save To Memory>Source Math>Destination M2>Save Now!).
8. Turn off the measurement parameters. Note that the mean value of the Math waveform is now at zero
9. Select dual in the Math setup dialog. Select Operator2 to be integral.

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 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 the Math trace now lists the units as C for Coulombs. So once units are redefined subsequent math operations show the correct units of measure.

### Conclusion

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

This completes the tutorial.