The Delay is the propagation time of a wave traveling through the transmission line. The Electrical Length is equal to the Delay times the speed of light in the vacuum and is a measure for the length of transmission line between the standard and the actual calibration plane. For a line with permittivity εrand mechanical length Lmech the delay and the electrical length are calculated as follows:

Electrical Length, Mechanical Length or Delay are coupled parameters. When one of them is changed, the other two follow.

For a non-dispersive DUT, the delay defined above is constant over the considered frequency range and equal to the negative derivative of the phase response with respect to the frequency (see mathematical relations). The length offset parameters compensate for a constant delay, which is equivalent to a linear phase response.

If a dispersive connector type (i.e. a waveguide; see Offset Modeldialog) is assigned to a test port that is related to a particular quantity, then the phase of the quantity is calculated taking dispersion effects into account.

The loss L is the attenuation of a wave traveling through the offset transmission line. In logarithmic representation, the loss can be modeled as the sum of a constant and a frequency-dependent part. The frequency dependence is essentially due to the skin effect; the total loss can be approximated by an expression of the following form:  

The DC loss LossDC, the reference frequency fref, and the loss at the reference frequency Loss(fref) are empirical parameters for the transmission lines connected to each port which can be entered into any of the dialogs in the Offset menu (see figure below). For a lossless transmission line, LossDC = Loss(fref) = 0 dB. In practice, the frequency-dependent loss often represents the dominant contribution so that LossDC can be set to zero.

The entries in the One-Way Loss section of the offset dialogs have the following meaning: DC loss LossDC(at DC), total loss at the reference frequency Loss(fref) (at Freq), reference frequency fref (Freq). Experimentally, the two loss values LossDC and Loss(fref) are determined in two separate measurements at a very low frequency (f --> 0) and at f = fref.

Offset parameters can be particularly useful if the reference plane of the calibration cannot be placed directly at the DUT ports, e.g. because the DUT has non-coaxial ports and can only be measured in a test fixture. Offset parameters can also help to avoid a new complete system error correction if a cable with known properties has to be included in the test setup.

• A positive length offset moves the reference plane of the port towards the DUT, which is equivalent to deembedding the DUT by numerically removing a (perfectly matched) transmission line at that port.

• A negative offset moves the reference plane away from the DUT, which is equivalent to embedding the DUT by numerically adding a (perfectly matched) transmission line at that port.  

The offset parameters are also suited for length and delay measurements; see Auto Length. In contrast to embedding/deembedding by means of the Channel – Mode – Virtual Transform functions, the offset parameters cannot compensate for a possible mismatch in the test setup.

Each offset parameter is assigned to a particular port. The delay parameters affect the phase of all measured quantities related to this port; the loss parameters affect their magnitude. An offset at port 1 affects the S-parameters S11, S21, S12, S31... Some quantities (like the Z-parameters) depend on the whole of all S-parameters, so they are all more or less affected when one S-parameter changes due to the addition of an offset length.

To account for the propagation in both directions, the phase shift of a reflection parameter due to a given length offset is twice the phase shift of a transmission parameter. If, at a frequency of 300 MHz, the electrical length is increased by 250 mm (λ/4), then the phase of S21 increases by 90 deg, whereas the phase of S11 increases by 180 deg. Equivalent relations hold for the loss.

If the trace is displayed in Delayformat, changing the offset parameters simply shifts the whole trace in vertical direction. The sign of the phase shift is determined as follows:

• A positive offset parameter causes a positive phase shift of the measured parameter and therefore reduces the calculated group delay.  

• A negative offset parameter causes a negative phase shift of the measured parameter and therefore increases the calculated group delay.  

The functions in the Offset menu can be used for balanced port configurations:

• If a balanced port configuration is active the logical and physical ports are shown in the Electrical Length, Mechanical Length and Delay dialogs.

• Offset parameters must be assigned to both physical ports of a logical port.

• Auto Length corrects the length offset of both physical ports of a logical port by the same amount.  

Auto Length is enabled if the measured quantity contains the necessary phase information as a function of frequency, and if the interpretation of the results is unambiguous:

• A frequency sweep must be active.

• The measured quantity must be an S-parameter, ratio, wave quantity, a converted impedance or a converted admittance.

The effect of Auto Length on S-parameters, wave quantities and ratios is to eliminate a linear phase response as described above. The magnitude of the measured quantity is not affected. Converted admittances or impedances are calculated from the corresponding Auto Length corrected S-parameters. Y-parameters, Z-parameters and stability factors are not derived from a single S-parameter, therefore Auto Length is disabled.  

The Auto Length function can be used for balanced port configurations as well. If the active test port is a logical port, then the same length offset is assigned to both physical ports that are combined to form the logical port. If different length offsets have been assigned to the physical ports before, they are both corrected by the same amount.  

Auto Length and Loss is enabled if the measured quantity contains the necessary phase information as a function of the frequency, and if the interpretation of the results is unambiguous:

• A frequency sweep must be active.

• The measured quantity must be an S-parameter, ratio, wave quantity, a converted impedance or a converted admittance.

The effect of Auto Length and Loss on S-parameters, wave quantities and ratios is to eliminate a linear phase response and account for a loss as described above. Converted admittances or impedances are calculated from the corresponding Auto Length and Loss corrected S-parameters. Y-parameters, Z-parameters and stability factors are not derived from a single S-parameter, therefore Auto Length and Loss is disabled.  

The loss is assumed to be given in terms of the DC loss LossDC, the reference frequency fref, and the loss at the reference frequency Loss(fref). The formula used in the Auto Loss algorithm is similar to the formula for manual entry of the loss parameters (see Loss parameters: Definition). The result is calculated according to the following rules:  

• The reference frequency fref is kept at its previously defined value (default: 1 GHz).  

• The DC loss c is zero except for wave quantities and for S-parameters and ratios with maximum dB magnitude larger than –0.01 dB.

• Auto Length and Loss for a wave quantity centers the corrected dB magnitude as close as possible around 0 dBm.

• Auto Length and Loss for S-parameters and ratios centers the corrected dB magnitude as close as possible around 0 dB.

The resulting offset parameters are displayed in the Electrical Length, Mechanical Length, and Delay dialogs.  

The Auto Length and Loss function can be used for balanced port configurations as well. If the active test port is a logical port, then the same offset parameters are assigned to both physical ports that are combined to form the logical port. If different offset parameters have been assigned to the physical ports before, they are both corrected by the same amount.