Using Math / Memory Operations

You can perform four types of math on the active trace versus a memory trace. In addition three statistics (Mean, Standard Deviation and Peak to Peak) can be calculated and displayed for the active data trace.

Note: Trace Math (described here) allows you to quickly apply one of four math operations using memory traces. Equation Editor allows you to build custom equations using several types of traces from the same, or different channels.

Data Math

All math operations are performed on linear (real and imaginary) data before being formatted. See the analyzer Data flow.

Data (or OFF) Does no mathematical operation.

Data / Memory - Current measurement data is divided by the data in memory. Use for ratio comparison of two traces, such as measurements of gain or attenuation. Learn more.

Data – Memory - Data in memory is subtracted from the current measurement data. For example, you can use this feature for storing a measured vector error, then subtracting this error from the DUT measurement. Learn more.

Data + Memory - Current measurement data is added to the data in memory. Learn more.

Data * Memory - Current measurement data is multiplied by the data in memory. Learn more.

8510 Mode - Learn more.

Trace View Options

Data Trace Displays ONLY the Data trace (with selected math operation applied).

Memory Trace Displays ONLY the trace that was put in memory.

Data and Memory Trace Displays BOTH the Data trace (with selected math operation applied), and the trace that was put in memory.

Interpolate

Note: The E5080A and M9485A do not support this function.

After performing a Data->Memory operation, memory interpolation controls whether the memory data is interpolated or not if the start frequency, stop frequency, or Number of Points is subsequently changed. Using the GUI control, interpolate applies to the currently active measurement. When using the remote interfaces (SCPI or COM), the commands apply to the specified measurement.

Note: Interpolate does not support the 8510 Mode.

The analyzer will return to a default interpolation state after a Preset, creating a new trace, or closing the analyzer application. The default interpolation state is set in the Preferences dialog by checking or unchecking the Memory: Interpolate ON is the default condition preference. The factory default is unchecked. The default can also be set using the remote interfaces (SCPI or COM).

When unchecked, after a Data->Memory operation the memory trace's x-y positions will not change if the start or stop frequency is subsequently changed. In addition, if the Number of Points in the sweep is changed after a Data->Memory operation, the memory trace will be invalidated and disappear. If the Number of Points is changed while using Data Math, the Memory trace will be invalidated and Data Math will be forced to the "Off" condition.

When checked, after a Data->Memory operation the memory trace's x-y positions will be interpolated if the start or stop frequency is subsequently changed. In addition, if the Number of Points in the sweep is changed after a Data->Memory operation, the memory trace will be interpolated.

Note: The analyzer will not extrapolate to stimulus values beyond the range that was present at the time of the Data->Memory operation. Instead, the Memory data will be invalidated if the stimulus values exceed the original range.

Note: If Interpolate is checked (ON) and stimulus conditions are different than they were at the time of Data->Memory operation, unchecking (OFF) Interpolate will cause the Memory trace to be either updated (using both original and current stimulus settings) or invalidated (if Number of Points changed since Data->Memory operation). The Memory trace will remain disabled until either Interpolate is checked (ON) or the stimulus settings corresponding to the Data->Memory operation are restored.

Data->New Trace

The Data -> New Trace allows several memory traces to be saved from the same trace data. Measurements made under different conditions can be compared. The following are two typical use cases:

Compare a DUT response before and after tuning.
Compare the response of two or more DUTs.

This feature copies the trace data from the active measurement into a new, independent trace. The new trace will not change when measurements are updated by a new sweep. The lowest-numbered available trace number is assigned. A new trace is created in the same channel and window.

Complex data and formatted data is copied from the original trace to the memorized (locked) trace.The following settings are also copied: markers, transform, phase offset, smoothing, parameter conversion, trace title, scattergram, scale, and trace format. The only softkeys disabled for a memorized (locked) trace are the measurement parameter softkeys (so that the measurement cannot be changed) and the Data->New Trace softkey. Save/Recall, however, is supported for memorized traces.

Trace Label

The new trace label is displayed in the Trace Annotation area as shown below:

Tr 2 - The first part of the label is the same as other traces; for example, Tr 2, Tr 3, etc.

Lock- The locked symbol indicates that the trace will not update from sweep to sweep.

MTr1.1 S11 - Displays the following information:

MTr1 - 1 Indicates the original trace number.

.1 - The number after period indicates the number of copies of the trace that exist after this new trace has been added.

S11 - Original trace parameter that was being measured when Data -> New Trace was pressed. The Trace Title feature allows the parameter name to be customized.

In the example above, Tr4 is copied from Tr3 and is the first copy.

X-Axis Label

If the memorized trace is shown in the same window as the original trace, and if the swept conditions have not changed, then the memorized trace will share x-axis labels with the original trace as shown below:

Ch1 sweep settings unchanged

Tr 1 (Yellow) - original trace

Tr 2 (Blue) - memorized trace

If the memorized trace is shown in the same window as the original trace but sweep settings have changed since it was created, then the memorized trace will be displayed on a separate line of x-axis labels. The memorized trace line will still show “ChX” where X is the channel number of the original trace. It also indicates that these are prior, locked stimulus settings.

Ch1 sweep settings changed

Tr 1 (Yellow) - original trace

Tr 2 (Blue) - memorized trace

If the memorized trace is shown in a different window than the original trace, and there are no other traces in that window from the original channel with the same swept conditions, then the memorized trace will be displayed on a separate line of x-axis labels.

Ch1 sweep setting changed or unchanged

Tr 3 (Yellow) - original trace in Window 2 from Ch2

Tr 2 (Blue) - memorized trace from Tr 1 and Ch1

Equation Editor

This new trace is also available in the Equation Editor for math operations. It will appear in the same way that other traces appear as shown below:

Learn more about Trace Math (scroll up)

(Data / Memory) and (Data - Memory)

(Data / Memory) and (Data - Memory) math operations are performed on linear data before it is formatted. Because data is often viewed in log format, it is not always clear which of the two math operations should be used. Remember: dividing linear data is the same as subtracting logarithmic data. The following illustrates, in general, when to use each operation.

Use Data / Memory for normalization purposes, such as when comparing S21 traces "before" and "after" a change is made or measurement of trace noise. In the following table, the Data/Mem values intuitively show the differences between traces. It is not obvious what Data-Mem is displaying.

S21 values to compare	Data/Mem	Data-Mem
0.5 dB and 0.6 dB	0.1 dB	-39 dB
0.5 dB and 0.7 dB	0.2 dB	-33 dB

Use Data - Memory to show the relative differences between two signals. Use for comparison of very small signals, such as the S11 match of two connectors.

In the following table, Data/Mem shows both pairs of connectors to have the same 2 dB difference. However, the second pair of connectors have much better S11 performance (-50 and -52) and the relative significance is shown in the Data-Mem values.

S11 values to compare	Data/Mem	Data-Mem
-10 dB and -12 dB	2 dB	-24 dB
-50 dB and -52 dB	2 dB	-64 dB

Data * Memory and Data + Memory

Use Data * Memory and Data + Memory to perform math on an active data trace using data from your own formulas or algorithms rather than data from a measurement. For example, if you want to simulate the gain of a theoretical amplifier placed in series before the DUT, you could do the following:

Create an algorithm that would characterize the frequency response of the theoretical amplifier.
Enter complex data pairs that correspond to the number of data points for your data trace.
Load the data pairs into memory with SCPI or COM commands. The analyzer maps the complex pairs to correspond to the stimulus values at the actual measurement points.
Use the data + memory or data * memory function to add or multiply the frequency response data to the measured data from the active data trace.

Note: The data trace must be configured before you attempt to load the memory.

Trace Statistics

You can calculate and display statistics for the active data trace. These statistics are:

Mean
Standard deviation
Peak-to-peak values

You can calculate statistics for the full stimulus span or for part of it by using User Ranges.

You can define up to 16 user ranges per channel. These user ranges are the same as the Search Domain specified for a marker search in that same channel. They use the same memory registers and thus share the same stimulus spans.

The user ranges for a channel can overlap each other.

A convenient use for trace statistics is to find the peak-to-peak value of passband ripple without searching separately for the minimum and maximum values.

The trace statistics are calculated based on the format used to display the data.

Rectangular data formats are calculated from the scalar data represented in the display
Polar or Smith Chart formats are calculated from the data as it would be displayed in Log Mag format. In Smith Chart format, the Trace Statistics dialog provides the option of displaying impedance in ohms.

See how to make Trace Statistics display settings.

How to activate Trace Statistics

Using Hardkey/SoftTab/Softkey

Press Math > Analysis > Statistics....

Trace Statistics dialog box help

See how to make Trace Statistics display settings.

Statistics Check to display mean, standard deviation, and peak to peak values for the active trace.

Span Specifies the span of the active trace where data is collected for a math operation. You can select Full Span, or define up to 16 user spans per channel with Start and Stop. You can also define the user spans from the Search Domain selector on the Marker Search dialog box.

User Start Defines the start of a user span.

User Stop Defines the stop of a user span.

Show Smith Chart statistics in Ohms Check this box to change statistics from Log Mag (dB) to impedance (ohms).

Learn more about Trace Statistics (scroll up)

Trace Deviation

You can calculate deviation from a least-best fit line. The choices are:

Off
Linear - Fit to 1st order curve minimizing RSS deviation.
Parabolic - Fit to 2nd order curve minimizing RSS deviation.
Cubic - Fit to 3rd order curve minimizing RSS deviation.

How to activate Trace Deviation