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How can I calculate the equivalent phase delay, as a function of frequency, for a given electrical delay as set on a Keysight Vector Network Analyzer?

Equivalent phase delay, based upon electrical delay is computed as:
θ°= Ftest * Delay * 360
Where:
θ° = Equivalent Phase
Ftest = Frequency (Hz)
Delay = Delay (seconds)
360 = Conversion factor, radians to degrees

Example:

Figure 1 is a PNG image acquisition from a Keysight PNA network analyzer.

  • Start Frequency 1.0GHz, Stop Frequency 2.0GHz, 201 Points
  • Full 2-Port Calibration via a Keysight electronic calibration module (ECal)
  • Single channel, two traces, one trace in each of two windows
  • Device Under Test - Keysight N4419AK20, 3' 3.5mm male to 3.5mm female cable assembly.
  • Upper Window, 'Tr1', S21, Format Phase, Delay = 0S (no electrical delay)
  • Lower Window, 'Tr2', S21, Format Phase, Delay = 3.623045-9S (delay applied automatically via the Marker Function - Delay selection on the PNA network analyzer).

PNA Screen Capture

Figure 1 - PNA Screen Capture, Single Channel, S21 Phase, Dual Window, Tr1 No Delay, Tr2 Auto Delay; View larger image

A partial sample of the acquired trace data / discrete data points for Tr1 and Tr2, as imported and processed within Microsoft Excel, are noted in Figure 2 below.

S21 Phase as Imported to Excel

Figure 2 – S21 Phase, Trace 1 (Tr1) & Trace 2 (Tr2), Partial Data, Points 1...28/201 as Imported to Excel; View larger image

Sample Calculation:

Equivalent Phase Delay, Frequency = 1.0 GHz.
θ° = Ftest * Delay * 360
θ° = 1E9 * 3.623045E-9S * 360°
θ° = 1304.2962°

Additional Notes:

The Keysight vector network analyzer default phase format wraps the phase at the limits of ±180°. The calculated equivalent phase shift must be manipulated for phase rotations in excess of 360° (which is equivalent to one wavelength). Thus the modulo* function is applied to the resultant data. Additionally, if the modulo function result is greater than 180° , then an additional 360° is subtracted from the result (i.e. from the remainder). If the result of the modulo function is less than 180°, then the remainder is the result.

*Modulo function calculates the remainder of division of one number, 'X', by another, 'Y'. Modulo is applied here as Modulo(X,Y) where X = computed phase and Y = 360˚.

Based upon the notes above, the equivalent insertion phase (θ°) @ 1.0 GHz = 1304.2962° is calculated as follows:

Applying the modulo function, modulo (1304.2962, 360) = 224.2962°.
Applying the rule:
IF
(Modulo (1304.2962, 360)) > 180
THEN
(Modulo (1304.2962, 360)-360)
ELSE
(Modulo (1304.2962, 360))

The THEN condition is true since modulo (1304.2962, 360) = 224.2962 (i.e. > 180°). Subtract 360° or,
Modified equivalent insertion phase = 224.2962° - 360°
Modified equivalent insertion phase = -135.7038°

The modified equivalent insertion phase at 1.0GHz with 3.623045nS delay = -135.7038°.

The original S21 phase parameter of Tr1 @ 1GHz with 0 nS delay = 134.5573˚ (from 'Exported PNA PRN S21 Phase Trace Data Tr1 & Tr2' in Figure 2 above). The Insertion Phase at 1.0 GHz with 3.623045nS delay (Tr2) = -1.1465˚ (again, from 'Exported PNA PRN S21 Phase Trace Data Tr1 & Tr2' in Figure 2 above).

The delayed phase ('Tr2' phase) is calculated as the sum of the Original phase (i.e. 'Tr1' phase, 0s delay, at a specified frequency) + Modified Equivalent Insertion Phase;
Final Phase with delay = Original phase + Modified Equivalent Insertion Phase
Final Phase = 134.5573˚ + -135.7038˚
Final Phase = -1.1465˚.
Final Phase, absolute, Tr2, based upon 3.623045nS @ 1GHz = -1.1465˚. Thus, correlation with the Phase data for 1GHz, Tr2, 3.623045nS delay.

The remainder of the phase correlation checks and related computations are noted below:

Phase correlation checks and related computations