Basic Behavioural and Device Models
At the system level, analysis and design of electronic circuits is based on the set of fundamental building blocks represented by their behavioural models. In the initial phase of the design it is important to validate the intended functionality of the ov
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Basic Behavioural and Device Models
At the system level, analysis and design of electronic circuits is based on the set of fundamental building blocks represented by their behavioural models. In the initial phase of the design it is important to validate the intended functionality of the overall circuit at the level of mathematics, without regard for the implementation details. Therefore, the knowledge of functionality of fundamental devices, namely a switch, voltage and current sources, and RLC devices as well as their respective impedances, is the prerequisite for the next phase in the design process. In this chapter we review these fundamental devices and their transfer functions.
2.1
“Black Box” Technique
The “black box” approach is based on the idea that in order to create systems’ behavioural model it is not necessary to know its exact internal structure, instead it is sufficient to know its stimulus/response (i.e. its I/O) transfer function. In the case of electronic circuits, the transfer function is found in terms of the input/output voltage/current characteristics both in time and frequency domains where the transfer function may be either linear or nonlinear. Therefore, in total, there are four possible I/O voltage/current transfer functions: 1. (Vin → Vout ): this relationship defines system’s “voltage gain” transfer function as vout = Av × vin
∴
Av = def
vout vin
V V
(2.1)
2. (Iin → Iout ): this relationship defines system’s “current gain” transfer function as iout = Ai × iin
∴
iout Ai = iin def
A A
(2.2)
3. (Iin → Vout ): this relationship defines system’s “resistance” transfer function as vout = R × iin
© Springer Nature Switzerland AG 2021 R. Sobot, Wireless Communication Electronics, https://doi.org/10.1007/978-3-030-48630-3_2
∴
vout R= iin def
V def = A
(2.3)
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2 Basic Behavioural and Device Models
4. (Vin → Iout ): this relationship defines system’s “gm ” transfer function as iout = gm × vin
∴
gm = def
iout 1 = R vin
A def =S V
(2.4)
In order to create complete model of a system, all four of the above transfer functions are equally important. We determine these I/O functions first by theoretical analysis then by the experiment. Therefore, the final model of a device is often created by a mixture of theoretical and experimental parameters. In general, to determine a system’s transfer functions, first we apply an input stimulus to one of the available terminals, then we collect the output data at the remaining terminals. We need to systematically choose one terminal as “input” and other as “output”, characterize its I/O transfer function, then proceed to choose another pair of terminals until all combinations are exhausted. In the following sections we look at some of the most typical experimental “signatures” of black boxes and the associated models of ideal elements.
2.2
Two-terminal Models
The two-terminal model is very useful because the I/O function simply shows “gain” in terms of I/O variables, namely voltage and current, where this I/O
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