Extract from:

Microwave System Design Tools and EW Applications, Second Edition, by Peter W East.
Publisher: Artech House Inc, January 2008.

Cascaded Mismatches

Applet Help

Applet Notes:

The applet applies complex combination analysis theory and calculates the VSWR and load power for a cascaded component chain. The chain comprises two variable electrical length transmission line components separated by a resistive attenuator; each are specified by VSWR and resistive insertion loss. The source and load are also specified by VSWR.
All the 32 possible impedance combinations of the five defining VSWRs are evaluated. The common linear combination approximation is also evaluated for comparison.
Two plots options are available from the drop-down menu. Plot 1 shows the VSWR for two combinations of components and Plot 2 shows the resulting power delivered to the load.
Only two (shown in red and blue) of the 32 impedance combinations are displayed at any one time for clarity. The Impedance Combinations drop-down menu allows examination of all 16 pair sets of impedance combinations. Entered at the bottom of the display are the component impedance values, based on a system characteristic impedance of 50Ω, for the currently displayed pair. All component impedances are sent to the Data Console when data is saved.
The transmission line component impedance that is displayed is the characteristic impedance of the equivalent loaded transmission line that produces the required mismatch as specified by the VSWR value selected. It is not equal to the VSWR-calculated mismatch impedance.
The frequency range is adjustable and the default chosen to exhibit frequency-dependent variation. Components 1 and 2 are characterized by different propagation time delays, defined by their electrical length. Shown and tagged in black are the results of using simple linear combination for comparison.
Moving the mouse in VSWR/Frequency space displays the plotted values referred to the mouse x-axis position. The display automatically scales to the data input.

User Notes:
Components are normally specified by VSWR. Actual impedances may be above or below the system characteristic impedance. Alternating high and low impedance values produce the worst-case mismatches. On the other hand, if all impedances were identical regardless of the system characteristic impedance design value, the chain would not produce a standing wave and so would appear matched.
The T-attenuator VSWR is not relevant when the attenuation is set to 0dB as the series resistors are effectively shorted and the parallel resistor is open-circuit. However, the attenuator resistor and characteristic impedance values are automatically adjusted to conform to the VSWR and real attenuation values selected.
The load impedance can be made reactive. In this case, the reactance range is only variable within a sensible range to conform to the VSWR setting.
For example, no reactive component is allowed if the load VSWR is set to 1.0, whereas large VSWRs can occur with very reactive loads.
Similarly, the transmission line component characteristic impedance is automatically adjusted to be compatible with the selected VSWR.
The applet shows that the generator source resistance affects the level of power transfer, but does not alter the match properties of the RF chain.
It also highlights the limited accuracy of the common linear combination method for estimating the result of cascading components.