Gain and phase ripples in an electronic-warfare (EW) receiver can lead to distortion, which in turn can degrade the bit-error-rate (BER) performance of the receiver. Fortunately, a straightforward analysis based on S-parameters can be performed by building upon the basic theory presented in ref. 1. This analysis first considers a general two-port linear bilateral network, then a two-port linear unilateral network (such as an amplifier, mixer, and isolator). In general, an amplifier operating in its linear region has reverse isolation (from output to input) that is usually twice the forward gain but is at least 18 dB (a power ratio of 0.0158). An amplifier's input and output VSWRs are usually on the order of 2.0:1 over its range of operating frequencies.

Mixers are three-port devices, with RF, intermediate-frequency (IF), and local-oscillator (LO) ports. Microwave mixers can be considered as two-port devices because the LO-to-RF isolation may be on the order of 25 dB or greater, and the LO-to-IF isolation may be on the order of 15 dB or greater. The RF-to-IF loss may vary from about 6 to 8 dB. The VSWR of the RF and IF ports may be as high as 2.5:1. Based on these conditions, it is assumed that mixers and isolators may be considered as two-port linear unilateral networks.

The transducer power gain of a linear, bilateral or unilateral two-port network is given in S-parameters as¹:

where:
S₂₁ = matched power gain of the network;
S₁₂ = reverse matched power gain of network;
G_S, G_L = complex source, load reflection coefficient, respectively;
S₁₁, S₂₂ = complex input, output reflection coefficients, respectively, of the network.

Equation 1 may be written as Eq. 2.

The second term in the denominator of Eq. 2 is defined as the "F" factor for convenience, where F is defined by Eqs. 3a, 3b, and 3c.

The "F" factor can be approximated by Eq. 3d.

The following inequalities can be used to simplify F:

S₁₂S₂₁§¤_s§¤_L ¡Ü 1, S₁₁§¤_gS₁₂S₂₁§¤_s§¤_L << 1, S₂₂§¤_L S₁₂S₂₁§¤_s§¤_L << 1 &gamma;

resulting in Eq. 3e.

From Eqs. 3b and 3c, Eqs. 3f and 3g can be derived:

For the case where |S₁₁¦£_s| << 1 with |S₁₂ | = |S₂₁| < 1 for a passive bilateral network, Eqs. 3f and 3g reduce to:

Substituting Eqs. 4a and 4b into Eq. 2, all but the first term yields:

where

¦È₁ = ¦µ₁₁ + ¦µ_g = 2¦Ðf(¦Ó₁₁ + ¦Ó_g);
¦È₂ = ¦µ₂₂ + ¦µ_L = 2¦Ðf(¦Ó₂₂ + ¦Ó_L);
¦È₃ = ¦µ₁₂ + ¦µ₂₁ + ¦È₁ + ¦È₂ = 2¦Ðf(¦Ó₁₂ + ¦Ó₂₁ + ¦Ó₁₁ + ¦Ó_g + ¦Ó₂₂ + ¦Ó_L)

The ¦Ó terms are proportion delays for the respective parameter.

Equation 2 can be written in terms of decibels as Eq. 7.

The last term on the right-hand side may be given in terms of natural logarithms by using Eq. 8.

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