The Virtual Transform submenu defines virtual networks to be added to/removed from the measurement circuit for a DUT with single ended or balanced ports. The submenu is available for analyzer models with arbitrary numbers of ports.
Embedding a DUT into a matching network
To be integrated in application circuits, high-impedance components like Surface Acoustic Wave (SAW) filters are often combined with a matching network. To obtain the characteristics of a component with an added matching network, both must be integrated in the measurement circuit of the network analyzer. The figure below shows a DUT with a single-ended and a balanced port that is combined with a real matching circuit and a physical unbalance-balance transformer (balun) in order to be evaluated in a 2-port measurement.
The idea of virtual embedding is to simulate the matching network and avoid using physical circuitry so that the analyzer ports can be directly connected to the input and output ports of the DUT. The matching circuit is taken into account numerically. The analyzer measures the DUT alone but provides the characteristics of the DUT, including the desired matching circuit. This method provides a number of advantages:
The measurement uncertainty is not impaired by the tolerances of real test fixtures.
There is no need to fabricate test fixtures with integrated matching circuits for each type of DUT.
Calibration can be performed at the DUT's ports. If necessary (e.g. for compensating for the effect of a test fixture) it is possible to shift the calibration plane using length offset parameters.
Deembedding a DUT from a matching network
Deembedding and embedding are inverse operations: A deembedding problem is given if an arbitrary real network connected to the DUT is to be virtually removed in order to obtain the characteristics of the DUT alone. Deembedding is typically used for DUTs which are not directly accessible because they are inseparably connected to other components, e.g. for MMICs in a package or connectors soldered to an adapter board.
To be numerically removed, the real network must be described by a set of S-parameters or by an equivalent circuit of lumped elements. Deembedding the DUT effectively extends the calibration plane towards the DUT ports, enabling a realistic evaluation of the DUT without the distorting network. Deembedding can be combined with length offset parameters.
The simplest case of single port deembedding can be depicted as follows:
The embedding/deembedding function in the Virtual Transform menu has the following characteristics:
Embedding and deembedding can be combined with balanced port conversion: the (de-)embedding function is available for single ended and balanced ports.
A combination of four-port and two-port networks (not necessarily both) can be applied to balanced ports; two-port networks can be applied to single ended ports.
A combination of four-port and two-port networks can be applied to any pair of single-ended ports. Moreover it is possible to combine an several port pairs in an arbitrary order (port pair (de-)embedding).
(De-)embedding at a single-ended and/or balanced port may be combined with ground loop (de-)embedding. A ground loop models the effect of a non-ideal ground connection of the DUT.
Transformation networks can be defined by a set of S-parameters stored in a Touchstone file or by an equivalent circuit with lumped elements.
The same networks are available for embedding and deembedding.
Port Overview... opens a dialog providing an overview of all analyzer ports with their reference impedances and transformation networks.
Deembedding/Embedding at Single Ended Port opens the configuration dialog for the single ended circuits and activates or deactivates (de-)embedding.
Deembedding/Embedding at Balanced Port opens the configuration dialog for the balanced port circuits and activates or deactivates (de-)embedding. These commands are enabled only after a balanced port configuration has been defined.
Ground Loop Deembedding/Embedding opens the configuration dialog for the ground loop circuits and activates or deactivates (de-)embedding.
Deembedding/Embedding at Port Pair opens the configuration dialog for the port pair circuits and activates or deactivates (de-)embedding.
Using Virtual Networks (Embedding/Deembedding)
Provides an overview of analyzer ports with their reference impedances and transformation networks (if (de-)embedding is active).
Each row in the Port Overview table corresponds to one logical or physical analyzer port; the number of rows in the different columns is equal to the number of balanced ports or physical test ports of the analyzer. The buttons open different dialogs for test port configuration:
Reference Impedance defines complex impedances for balanced test ports.
Deembedding at Balanced Port and Embedding at Balanced Port show the 4-port transformation networks to be numerically added or removed at balanced (logical) ports. Off denotes that no (de)embedding operation is performed.
Deembedding at Single Ended Port and Embedding at Single Port show the 2-port transformation networks to be numerically added or removed at single ended (physical) or balanced (logical) ports. Off denotes that no (de)embedding operation is performed.
A ground loop cannot be assigned to a logical or physical analyzer port, so ground loop (de-)embedding is not shown in the Port Overview dialog. The same applies to port pair (de-)embedding which involves pairs of physical ports.
In the Port Overview dialog, it is possible to select a combination of 4-port and 2-port networks to be numerically added/removed at balanced (logical) ports, and to select 2-port networks at single ended (physical) ports. The following example shows the full configuration for a four-port analyzer where the physical ports 1 and 3 form a balanced port with the logical port no. 1 and the remaining ports 2 and 4 are single ended.
The port overview configuration above corresponds to the measurement circuits shown in steps 1 to 5 below.
The different steps for deembedding and embedding are carried out in the following order (the figure also contains possible ground loop and port pair (de-)embedding stages which are not shown in the Port Overview dialog):
This means that the real networks are removed before virtual networks are added. For a single balanced port with all single ended and balanced port (de-)embedding networks enabled, the 4 (de-)embedding steps are carried out in the following order:
Initial situation: DUT embedded in 2-port and 4-port networks (only 1 port shown)
Deembedding at single ended port
Deembedding at balanced port
Embedding at balanced port
Embedding at single ended port
Changes the reference impedances of the analyzer ports. This is often referred to as renormalization of port impedances. Renormalization means that the measurement results measured at 50 Ω (75 Ω) are converted into results at arbitrary port impedance.
Renormalization of the physical port impedances affects e.g. S-parameters and wave quantities in Power representation.
Renormalization of the balanced port impedances affects all measured quantities (Trace – Measure) that the analyzer provides for balanced ports.
The default reference impedance of a physical port is equal to the reference impedance of the connector type assigned to the port (50 Ω or 75 Ω). It can be defined as a complex value.
For balanced ports it is possible to define separate complex reference impedances for differential and for common mode.
The default values for the balanced port reference impedances are derived from the default reference impedance of the physical analyzer ports (Z0 = 50 >Ω):
The default value for the differential mode is Z0d = 100 Ω = 2*Z0.
The default value for the common mode is Z0c = 25 Ω = Z0/2
Renormalization can be based on two alternative waveguide circuit theories. The conversion formula of both theories differ only if the reference impedance of at least one test port has a non-zero imaginary part.
Conversion formula for wave quantities and S-parameters
Renormalization transforms the "raw" S-matrix S0 for the default reference impedances Z0i (with physical port number index i = 1, 2...n) into a "renormalized" S-matrix S1 for the modified reference impedances Z1i. In terms of raw and renormalized wave quantities a0i, b0i and a1i, b1i, S0 and S1 are defined as follows:
The renormalized wave quantities (a1 and b1) and the S-matrix S1 can be calculated from S0 and the reference impedances Z0i, Z1i.according to two alternative waveguide circuit theories.
1. Travelling waves
In the model of Marks and Williams ("A General Waveguide Circuit Theory"), the wave quantities a and b are transformed as follows:
The renormalized S-matrix S1 is calculated as
,
with the unit matrix E and two additional matrices with the elements
.
1. Power waves
In the model of Kurokawa ("Power Waves and the Scattering Matrix"), the wave quantities a and b are transformed as follows:
In true differential mode, a renormalization formula for the balanced wave quantities is needed; refer to Wave Quantities and Ratios.
Remote control:
SENSe:PORT<phys_port>:ZREFerence <real> [,<imaginary] SENSe:LPORT<log_port>:ZCOMmon <real> [,<imaginary] SENSe:LPORT<log_port>:ZDIFferent <real> [,<imaginary] CALCulate<Chn>:TRANsform:IMPedance:RNORmal TWAVes | PWAVes
Selects a 2-port transformation network for single port (de-)embedding, defines its parameters, assigns it to a physical port and enables (de-)embedding. Single port (de-)embedding can be used for balanced (logical) as well as for single ended (physical) ports. The two dialogs for deembedding and embedding are identical except for their inverse effect.
The dialogs contain the following control elements:
Physical Port is the physical analyzer port for the added or removed circuit. The transformation networks are defined such that the physical analyzer test port is connected to the left of the circuit; the DUT port is on the right side.
(De-)embed DUT enables or disables the (de-)embedding function.
Transformation Network contains all available 2-port networks (see below). Networks are either defined by lumped elements or by means of imported S-parameter data. The active network appears in inverse colors. The element parameters (C, R, L) for the selected network are displayed on the right side.
Read Data From File... is enabled as long as the 2-Port Data network is active. This network is defined by its S-parameters stored in a two-port Touchstone file (*.s2p). No additional parameters are required. In case the port number conventions of the loaded two-port Touchstone file differ from NWA conventions (see description of Physical Port above), it is possible to Interchange Port Numbers of s2p File.
Set to Ideal Through is enabled as long as the 2-Port Data network is active. An imported S-parameter set is replaced by the S-parameters of an ideal through connection, which eliminates the transformation network.
Circuit models for 2-port networks
The lumped element 2-port transformation networks for (de-)embedding consist of the following two basic circuit blocks:
A capacitor C connected in parallel with a resistor.
An inductor L connected in series with a resistor.
The 2-port transformation networks comprise all possible combinations of 2 basic blocks, where one block represents a serial, the other a shunt element. In the default setting the resistors are not effective, since the serial Rs are set to 0 Ω, the shunt Rs are set to 10 MΩ.
The first network is defined by its S-parameters stored in an imported two-port Touchstone file (*.s2p). No additional parameters are required.
The following networks are composed of a serial C or L (as seen from the test port), followed by a shunt C or L. They are named Serial C, Shunt C / Serial C, Shunt L / Serial L, Shunt C / Serial L, Shunt L.
The following networks are composed of a shunt C or L (as seen from the analyzer port), followed by a serial C or L. They are named Shunt C, Serial C / Shunt C, Serial L / Shunt L, Serial C / Shunt L, Serial L.
Adding a virtual network to a single-ended port
Removing a virtual network from a single-ended port
CALCulate<Ch>:TRANsform:VNETworks:SENDed... MMEMory:LOAD:VNETworks<Ch>:SENDed:DEEMbedding<Ph_pt> '<file_name>' MMEMory:LOAD:VNETworks<Ch>:SENDed:EMBedding<Ph_pt> '<file_name>'
Selects a 4-port transformation network for balanced port (de-)embedding, defines its parameters, assigns it to a physical port and enables (de-)embedding. The two dialogs for deembedding and embedding are identical except for their inverse effect. The dialogs are available only after a balanced port configuration has been defined.
Transformation Network contains all available 4-port networks (see below). Networks are defined by lumped elements or by means of imported S-parameter data. The active network appears in inverse colors. The element parameters (C, R, L) for the selected network are displayed on the right side.
Read Data From File... is enabled as long as one of the networks involving two-port or four-port S-parameter data is active. The S-parameters are read from two-port (*.s2p) or four-port (*.s4p) Touchstone files. Each two-port file can be assigned to one of two different physical ports, to be selected by means of the Phys. Port radio buttons. In case the port number conventions of the loaded two-port Touchstone file differ from NWA conventions (see description of Physical Port above), it is possible to Interchange Port Numbers of s2p File.
Set to Ideal Through is enabled as long as one of the networks involving two-port or four-port S-parameter data is active. An imported S-parameter set is replaced by the S-parameters of an ideal through connection, which eliminates the transformation network.
Circuit models for 4-port networks
The lumped element 4-port transformation networks for (de-)embedding consist of the following two basic circuit blocks:
The transformation networks comprise various combinations of 3 basic circuit blocks, where two blocks represent serial elements, the third a shunt element. In the default setting the resistors are not effective, since the serial Rs are set to 0 Ω, the shunt Rs are set to 10 MΩ. Moreover, the serial elements can be replaced by imported 2-port S-parameters, or the entire transformation network can be described by imported 4-port S-parameters.
The first network is defined by its S-parameters stored in an imported four-port Touchstone file (*.s4p). No additional parameters are required.
The following networks are composed of a shunt C or L and two serial elements, described by means of imported 2-port S-parameters. They are named Serial 2-port, Shunt C / Serial 2-port, Shunt L / Shunt L, Serial 2-port / Shunt C, Serial 2-port.
The following networks are composed of two serial Cs or Ls (as seen from the analyzer test port), followed by a shunt C or L. They are named Serial Cs, Shunt C / Serial Cs, Shunt L / Serial Ls, Shunt C / Serial Ls, Shunt L.
The following networks are composed of a shunt C or L (as seen from the analyzer test port), followed by two serial Cs or Ls. They are named Shunt C, Serial Cs / Shunt C, Serial Ls / Shunt L, Serial Cs / Shunt L, Serial Ls.
Adding a virtual network to a balanced port
Removing a virtual network from a balanced port
CALCulate<Ch>:TRANsform:VNETworks:BALanced... MMEMory:LOAD:VNETworks<Ch>:BALanced:DEEMbedding<Log_pt> '<file_name>', PMAIn, PSECondary MMEMory:LOAD:VNETworks<Ch>:BALanced:EMBedding<Log_pt> '<file_name>', PMAIn, PSECondary