Multistage Interface
Over the time we have developed what is known as “top-to-bottom than bottom-to-top design flow”, that is to say a complicated system is designed hierarchically; during its development stage systems are often split into more than ten levels of hierarchy. O
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Multistage Interface
Over the time we have developed what is known as “top-to-bottom then bottom-to-top design flow”, that is to say a complicated system is designed hierarchically; during its development stage systems are often split into more than ten levels of hierarchy. Once the hierarchy chain is established and each of the stages is replaced by its equivalent Thévenin or Norton model, each of the blocks is considered to be a “black box” described by its input and output impedances and its transfer function. In this section we review basic interface models.
3.1
System Partitioning Concept
We appreciate the elegance and efficiency of the system level approach once we realize that each output signal generated by “driving stage” (or simply “the driver”) is received as the input signal by the “loading stage” (or simply “the load”). It is important to understand that except for the first and the last element in the chain, by itself, each stage is both driver (relative to its neighbour down the signal path) and load (relative to its neighbour up the signal path). For the purpose of the signal transmission, the internal structure of each stage is not relevant; indeed, it is only important to know the following: 1. 2. 3. 4.
Vout : amplitude of voltage (or current) signal generated by the driver, Zout : output impedance of the driver, Zin : input impedance of the load stage, and A: gain of each individual stage.
Conceptually, these driver–load relationships are used to model the signal transfer at each of the interface points. By doing so, at the conceptual level, analysis of a complicated system is reduced to repeated calculations of a simple voltage/current divider at each of the interfaces. The system partitioning enables us to calculate, for example, the total gain of a system, Fig. 3.1, as a product of the individual gains of each stage, as A = A1 × A2 × A3 × · · · × An
(3.1)
where gain of each stage is found by definition as the output to input signal ratio
© Springer Nature Switzerland AG 2021 R. Sobot, Wireless Communication Electronics, https://doi.org/10.1007/978-3-030-48630-3_3
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3 Multistage Interface
System
Rs
v out RL
vs
1.
vs
2.
v1
v2
v1
A1
...
3.
v2
A2
n
v3
A3
v out
...
An
Fig. 3.1 System partitioning based on voltage divider model at interface planes between two subsequent stages
A1 =
v1 ; vS
A2 =
v2 ; v1
A3 =
v3 ; v2
···
An =
vOU T vn−1
(3.2)
which is to say that v1 v2 v3 vOU T vOU T A = × × × ··· × = vS v1 v2 vn−1 vS
(3.3)
In addition, if the gain of each stage is expressed in decibels, then the total gain is simply the sum of the gains, as AdB = A1dB + A1dB + · · · × AndB
(3.4)
This general system partitioning idea enables us to perform rapid analysis “by inspection”, which gives us not only fast answers but also the insight into fundamental limits of the circuit topology under consideration. Routinely, the back of the envelope “rough” estimates are within less than 10% difference relative to the “exact” results derived by simulatio
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