#### Stability Factor...

Opens a dialog to select one of the three two port stability factors K, m 1 or m 2.

The Stability dialog provides the following settings:

- Stability Factor selects the stability factor to be calculated; see definitions below.

- Used Test Ports selects the test port number of the analyzer to be connected to the input (DUT Input) and the output of the DUT (DUT Output). The ports can be arbitrary, however, the stability factor calculation is based on 2-port reflection and transmission S-parameters so that the input and output port numbers must be different.

- The Port Topology panel is analogous to the corresponding panel in the More S Parameters
  dialog. Stability factors can be calculated for unbalanced ports only. If a balanced port configuration is selected, the analyzer generates an error message.

Values of any of the stability factors less than 1 indicate potential instability.

Definition of stability factors and stability criteria

The stability factors K, m 1 and m 2 are real functions of the (complex) S-parameters, defined as follows:

where denotes the complex conjugate of S.

Stability factors are calculated as functions of the frequency or another stimulus parameter. They provide criteria for linear stability of two-ports such as amplifiers. A linear circuit is said to be unconditionally stable if no combination of passive source or load can cause the circuit to oscillate.

- The K-factor provides a necessary condition for unconditional stability: A circuit is unconditionally stable if K>1 and an additional condition is met. The additional condition can be tested by means of the stability factors m 1 and m 2.

- The m 1 and m 2 factors both provide a necessary and sufficient condition for unconditional stability: The conditions m 1>1 or m 2>1 are both equivalent to unconditional stability. This means that m 1 and m 2 provide direct insight into the degree of stability or potential instability of linear circuits.

References: Marion Lee Edwards and Jeffrey H. Sinsky, "A New Criterion for Linear 2-Port Stability Using a Single Geometrically Derived Parameter", IEEE Trans. MTT, vol. 40, No. 12, pp. 2303-2311, Dec. 1992.

Remote control: | CALCulate<Ch>:PARameter:MEASure "<Trace_Name>", "KFAC21" | "MUF121" | "MUF221" | ... [SENSe<Chn>:]FUNCtion[:ON] "...:POWer:KFACtor | MUFactor1 | MUFactor2" Create new trace and select name and measurement parameter: CALCulate<Ch>:PARameter:SDEFine "<Trace_Name>", "SY11" | "SY12" | "SY21" | "SY22"

#### Imbalance...

Opens a dialog to select the imbalance for balanced ports.

Definition of imbalance parameters

An ideal unbalance-balance transformer (balun) converts an unbalanced signal into a balanced one and vice versa. When it is driven with an unbalanced signal at its physical port k, unbalanced signals with equal amplitude and opposite phase appear at the physical ports m and n.

This means that the ratio –Skm/Skn of the physical transmission coefficients of an ideal balun equals to 1. This ratio is called imbalance; it is a measure for the deviation of the balun from ideality. The definition of the imbalance of a DUT with one or two balanced ports and physical port numbers m < n, k < l is given below.

- The imbalance of a DUT with a single ended logical input port i and a balanced logical output port j is defined as Imb ij = –Skm/Skn and Imb ji = –Smk/Snk.

- The imbalance of a DUT with a balanced logical input port i and a balanced logical output port j is defined as Imb ij = –(Skm– Skn)/(Slm– Sln) and Imb ji = –(Smk– Snk)/(Sml– Snl).

In general the imbalance is a quantity with two numeric indices numbering the logical output port and the logical input port of the DUT during the measurement (Imb<out><in>).

The Imbalance dialog provides the following settings:

- Imbalance selects the imbalance parameter Imb<out><in> to be measured.

- Balanced and Measured Ports
  opens the dialog of the same name to define the properties of the test ports. Single-ended (unbalanced) impedance parameters are assigned to the physical test ports of the analyzer. Balanced impedance parameters are assigned to logical test ports. Selecting a balanced port configuration with logical test ports means that the unbalance-balance conversion
  is switched on and that the analyzer provides mixed mode parameters
  . A unbalance-balance conversion is a prerequisite for the calculation of imbalance parameters.

Remote control: | CALCulate<Ch>:PARameter:MEASure "<Trace_Name>", "IMB21" | "IMB12" ... Create new trace and select name and measurement parameter: CALCulate<Ch>:PARameter:SDEFine "<Trace_Name>", "IMB21" | "IMB12" ...

#### All S-Params

Displays all S-parameters S<out><in> that the analyzer can calculate according to its port configuration. Reflection parameters Sii are displayed in Smith charts; transmission parameters are displayed in Cartesian (dB Mag) diagrams. For a four-port analyzer with four single-ended ports:

A n-port analyzer provides n2 independent S-parameters S<out><in>. If a balanced port configuration is defined, the normal S-parameters are replaced by mixed mode parameters
.

Remote control: | –