**Introduction**

Phase shifters are a key component of systems such as phased arrays. This is due to the fact that they allow for the electronic steering of the antenna beam [1]. While there are many different types of phase shifters such as switched filter and vector modulator, the type we will consider in this post uses varactor diodes.

Varactor diode based phased shifters have been used for many decades and have been analyzed extensively [2]. They benefit from being very simple circuits that can achieve wide bandwidths. However, what has been not been analyzed is the effects on insertion loss from aging in the varactor diodes. This short analysis outlines some of my findings on the insertion loss and phase changes that will occur as a result of aging effects in varactor diodes. The aging effects will be represented by variations in the equivalent circuit model of the varactor diode. Namely, it will be shown that the insertion loss of a single stage (one diode) will change in response to changes in the device capacitance over an expected end of life range.

**Diode Model and Simple Phase Shifter**

An analysis of the equivalent circuit of a varactor diode was given in a prior post, but we will briefly discuss it here. Consider the circuits in Figure 1. A loaded line phase shifter using a shunt diode and the diode equivalent circuit are shown in 1a and 1b [3]. Note that the varactor diode is represented by Cp (diode package capacitance), Lp (diode package inductance), Rs (diode intrinsic series resistance), and C(V) which is the diode voltage dependent junction capacitance [4]. For this analysis, we can ignore the packaging effects so that Cp and Lp are eliminated from the model. A further simplification is to ignore Rs, though this effect can be included in a separate analysis. After the simplifications, we are left with a diode phase shifter as show in Figure 1(c).

*Figure 1. Schematics of (a) transmission line type diode phase shifter, (b) varactor diode equivalent circuit, and (c) simplified diode phase shifter model.*

The insertion loss of a shunt diode is given by 10Log10(1+b2/4) and the phase shift is given by –tan-1(b/2). Where, b is the normalized shunt susceptance of the capacitor. Using this formula, it is possible to build a analysis which shows the effect of diode variations. Consider Table 1. It shows the capacitance variation of typical varactor diode which changes from 1 to 4pF which provides a phase shift range of 18.5 to 53.2 degrees and an insertion loss variation of 0.5 to 4.4dB. From this analysis, it is possible to obtain an expected insertion loss change as a function of capacitance change DIL/DC (IL= Insertion Loss and C=capacitance). For an End Of Life (EOL) diode capacitance change is 25%, and an assumed starting capacitance of 2pF which is in the middle of the range for the capacitor, it is possible to have 0.66dB of insertion loss variation.

*Table 1. Spreadsheet analysis of the effects of capacitance variation on phase shifter insertion loss.*

**Conclusions and Additional Work**

This analysis shows that for a single diode phase shifter, it is possible to get 0.66dB of insertion loss variation. For a multiple stage phase shifter, this effect is additive in worst case. Therefore a six stage phase shifter may experience a 3.96dB variation in insertion loss due to end of life diode aging effects.

To say the least, much more investigation should be conducted on this topic. Some specific items that could be investigated are the addition of other model elements to more fully capture the varactor diode model. For instance the series resistance and parallel capacitance could be included in the diode model. It is unclear if these addition circuit elements will increase the effect of circuit aging on insertion loss and phase variation or somehow dampen the effects.

**References**

[1] R. Sturdivant, M. Harris, *Transmit Receive Modules for Communication and Radar Systems* (Norwood, MA: Artech House, 2015).

[2] Garver, R.V., “360° Varactor Linear Phase Modulator,” *IEEE Transactions on Microwave Theory and Techniques*, March 1969, pp. 137 – 147.

[3] George H. Stauffer, “Finding the Lumped Element Varactor Diode Model,” *High Frequency Electronics*, November 2003.

[4] Skyworks Application Note: Varactor Diodes.

Where does the figure of 25% in “End Of Life (EOL) diode capacitance change is 25%” come from?

Hi John,

As I recall, we were given that from the supplier of the diode. However, I don’t have the documentation on it any longer. My suggestion, if you want to do End Of Life (EOL) simulations, then it is best to confirm the diode variation with you diode supplier.

Rick