Before you begin to design a system with RF front end you need to create a system specification. To that end, you need to know the different RF system parameters and what they mean. The usual step to design an RF system is to have an initial design sketch. The sketch should include all the components such as mixers, filters, amplifiers, antenna etc. But knowing the component is not adequate. You need to know have their specification and performance parameters.

A RF system or analog front end consists of components in the chain up to the transducer usually an antenna. Each of the components such as mixers, amplifiers etc are quoted with gain, noise figure etc and each component are described with parameters such as Z, Y, ABCD or S parameters. Usually at low frequency Z, Y and ABCD parameters are used while S parameters are used for microwave frequencies circuits.

An example block diagram of an RF system is shown below.


 Any analog component in the chain such as an amplifier can be described with two port network parameters such as Z parameters, Y paramters, S parameters etc as shown below.


Thus, RF designer must have knowledge about many parameters for initial circuit design. Gain, stability, noise figure and noise factor, phase noise, non-linearities and distortion, dynamic range are some of the parameters that RF designer require to make an initial design.

The important RF design parameters are as follows.
  • Gain 
  • Stability
  • Matched Gain Parameters
  • Nonlinearity Parameters
  • Noise Figure
  • Phase Noise
  • Dynamic Range
These RF parameters will be explained in these and following tutorials. After these a RF design of real system is illustrated which uses the concept learned. In this post, the Gain, stability and matched gain parameters will be explained.

Gain

The gain parameters are power gain, current gain, voltage gain, transconductance gain, transimpedance gain. These parameters are related to circuit current and voltages. Either power gain, current gain or voltage gain can be considered as design variables. In circuit design where maximum power transfer is desired when connecting antenna to the front end receiver, power gain is chosen as the design variable. A mismatch in impedance between the components causes signal loss and hence signal loss. On the other hand the current and voltages gain are design parameters if the receiver stages are implemented on a single chip.

Power Gain

There are three important specification for power gain- operating power gain, available power gain and transducer power gain. These are all based on average signal magnitude instead of instantaneous and are measure of the efficiency of power transfer by the two port network.

Consider a two port network as shown below.


Here we have a source Vs with source impedance Zs supplying a voltage V to a two port component whose Scattering matrix is [S] and/or chain matrix parameters[ABCD]. The output from this component is Vo and the load impedance is ZL.

In terms of power one important parameter is the transducer power gain (gT). It is the ratio of power delivered to the load(PL) to the power available from the source(Pavs). Now if ⌈IN and ⌈OUT are the input and output reflection coefficient that characterizes the input and output impedenace matching at the input and output of the two port network and ⌈S and ⌈Lare the source and load reflection coefficients then transducer power gain (gT). is,


where S21 and S22 are the S matrix parameters which can be obtained from vector network analyzer.

The transducer power gain (gT) can also be expressed using [ABCD] parameters using the relation between S parameters and ABCD parameters. The transducer power gain (gT) using ABCD parameter is as follows:


The transducer power gain(gT) depends on the load and source reflection coefficients which in turn depends on the source and load impedance.

If the input and output impedances are matched then available power gain(gA) can be defined. It is the ratio of the power available from the two-port network and the power available from the source (PAVS).

Stability

 In RF design, one speaks of conditional and unconditional stability of two port network.  Given a two port network or component we start with specification of source and load impedance. These are generally given to us or are known quantities. Once we know these, find out the input and output reflection coefficients ⌈IN and ⌈OUT. If these reflection coefficients are less than unity for all ranges of load and source impedances then the two port network is said to be unconditionally stable. But the reflection coefficients are less than unity only for a range of load and source impedances then the two port network component is said to be conditionally stable.

An unstable condition happens when there is oscillation of signal and this happens if the real part of impedances are negative. So for example, in case of conditional stability, if there is impedance value(source or load) that is outside of the specific range of impedance, the real part is negative and this creates oscillation.

There are equation for testing conditional and unconditional stabilities. These are as follows.

Conditional Stability test equation,



Unconditional Stability test equation given by Rollet’s condition,



 Another equation for testing unconditional stability is the μ test which is as follows,



The difference between using μ test and Rollet’s condition for checking unconditional stability is that with μ test you can check and compare two devices for stability.

Matched Gain Parameters

Consider the equation for transducer power gain again,




In this equation, we can dissect and define the following gain factors terms,

The gain factor for source matching network(gs), the gain factor of the designed two port network(go) and gain factor the load matching network(gL),


Condition for Maximum Power Transfer

For the maximum power transfer, the input impedance of the two-port network must be conjugate matched to the impedance of the source-matching network, and the output impedance of the two-port network must be conjugate matched to the impedance of the load-matching network.

That is:


If these matching conditions are not met at either the input or the output of an external image-reject or channel select filter, the passband and stopband characteristics of the filter will exhibit loss and ripples.

The next tutorial on RF system design will be about Nonlinearity parameters, noise figure, phase noise and finally dynamic range.

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