### Introduction

The instrument gives you the ability to perform arithmetic operations (addition, subtraction, multiplication, division) on the results of two parameter measurements. Alternatively, you can apply math to a single parameter (for example, invert or rescale). By customizing parameters in this way, you can effectively extend the range of parameter measurements based on your particular needs. In this tutorial we will use parameter math to measure the power delivered to a load based on the measured rms voltage and the known load resistance.

### Equipment Required

WaveRunner 6Zi series oscilloscope

Coaxial cable

### Initial Setup

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

- Connect a coaxial cable from channel 1 to the Aux connector on the front panel.
- Recall the default setup: File pull down > Recall Setup> Recall Default.
- Turn off channel 2 by pressing the button marked 2 in the vertical control group on the front panel twice.
- Set the input coupling on Channel 1 to be 50 Ohms: Touch or click the channel 1 annotation box>touch or click on the coupling field >select DC 50 Ω.
- Set up the Aux output to be the Fast Edge signal. Utilities pull down > Utilities Setup >Aux Output Tab>touch or click on Fast Edge. The Fast Edge signal is a 5 MHz, 450 mVp-p, square wave.
- Auto Setup the scope: Press the Scope Setup button then select Auto Setup from the fly-out menu.
- This completes the initial setup. The scope display should be similar to Figure 1.

### Setting Up the Basic Measurement

Turn on measurements by using the Measure pull down menu. Select Measure Setup. The measure dialog box will open as shown in Figure 2. Click or touch on the Show Table checkbox. This will display the default parameters Ampl(itude) of C1 and Freq(uency) of C1. We will measure the rms voltage of C1 and then derive the power delivered to the 50 Ohm load resistor in the input channel.

Touch or click on the P1 tab of the Measure dialog box. Touch or click on the Measure field, the Select Measure Scroll box will appear. Scroll down to the parameter RMS and select it. The parameter P1 will now be measuring the rms voltage of the waveform in channel C1 as shown in Figure 3.

### Using Parameter Math to Square the RMS reading

Click or touch the P2 tab on the Measure dialog box. Select math on parameters under the Type selections on the left hand side of the dialog box. Touch the Math Operator field and the Select Measurement scroll box will display the available parameter math choices as shown in Figure 4. Select P Product, the Select Measurement scroll box will close. On the P2 tab set Source 1 and Source 2 to be P1.

The number of selections shown will be dependent on the option content of the oscilloscope. The minimum available parameter math selections are:

Symbol | Name | Description |

P_{const} | P Const | Set the parameter to a constant value |

P_{n}- P_{m} | P Difference | Difference between two input parameter values |

1/P_{n} | P Invert | Invert the input parameter (reciprocal) |

P_{n} * P_{m} | P Product | Calculate the product of two parameters |

P_{n} ÷ P_{m} | P Ratio | Compute the ratio of two parameters |

y = ax + b | P Rescale | Rescale parameter: a*(parameter value) + b |

P_{n} + P_{m} | P Sum | Adds two parameters |

We have set parameter P2 to be the product of P1*P1 or P1^{2} . This will now read the mean squared value of the channel 1 (C1) waveform.

### Using Parameter Rescale to Divide by a Constant

To complete our calculation we need to divide the mean squared voltage reading by the resistance of the channel input (50 Ohms in this case). We can do that with the parameter rescale function. Touch or click on the P3 tab of the Measure dialog box. Set the Type to be math on parameters, the source to be P2, and the Math Operator to be P Rescale. On the right hand side of the P3 tab the Rescale tab will be displayed. Double touch or double click the First multiply by field, a pop keypad will be displayed, enter ‘.02’. This is equivalent to dividing the mean squared voltage by 50.

### Setting Up the Units of the Computed Parameter

Click or touch the Overide units check box. The Output units box will appear. Double touch or double click, a pop up keyboard will be displayed. Type in “W” for Watts. This will set the output units to Watts as shown in Figure 5. P3 is now reading the power dissipated by the 50 Ohm load resistor in channel 1.

Using parameter math you can calculate parameters which are not available in the scope based on those that are. Here are some examples:

Crest Factor (Peak(max) /rms)

Apparent Power (Vrms* I rms)

Power factor (real power/ apparent power)

RPM (frequency * 60)

Wavelength (3*10^{8} /frequency)

Parameter math extends the usefulness of LeCroy oscilloscopes allowing the user to define custom parameters as needed.

This completes the tutorial.