Download Circuits and Systems Design Automation of Analog VLSI

Prof. D. Zhou
UT Dallas
Analog Circuits Design Automation
1
 Mathematical equations of a circuit
 Use KCL (or KVL) to establish the currents relationship
among the branches associated to each node
 Use device (circuit element) I-V relationship to obtain a set of
equations in which node voltages are the variables
 The number of equations equals the number of variables
 The analysis based on this method is called node analysis
 If there is a voltage source between two nodes, the current
through this voltage source is unknown and it should be
considered as a new variable.
 In this case the voltages across the corresponding nodes provides an
extra relation to be used, which gives an additional equation.
Analog Circuits Design Automation
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 Linear system
 When the equations describing the circuit are linear
equations or linear differential equations, the circuit is a
linear system
 A linear system:
 𝑋 = A𝑋 + B𝑢
 𝑌 = C𝑋
where X is a variable, u is an input and Y is an output
vector, respectively.
Analog Circuits Design Automation
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 A linear system can be transformed into frequency
domain by using Laplace transform
 𝑋 𝑠 = (Is − A)−1 B𝑢(𝑠)
 𝑌(s) = C𝑋(s)
 Transfer function can be written as
 𝑓 𝑠 =
𝑁(𝑠)
𝐷(𝑠)
where 𝑁(𝑠) and 𝐷 𝑠 are polynomial functions of 𝑠.
Analog Circuits Design Automation
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 A linear system usually will be used as an approximation
of the real system.
 The case of small signal situation
 Basically it is a first order approximation of Taylor expansion
series.
 Only for a linear system Laplace transform can be used.
 Only for a linear system a transfer function is defined
Analog Circuits Design Automation
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 How to relate circuits parameter or process variations to
the circuit performance
 Circuit parameters will appear in A, B, and C.
 Circuit parameters will appear in the coefficients of 𝑁 𝑠 and
𝐷(𝑠).
 Process variation will affect A, B, C or consequently 𝑁(𝑠) and
𝐷(𝑠).
Analog Circuits Design Automation
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Performance bound of a linear system
 For a function
𝑓 𝑠 = 𝑎0 + 𝑎1 𝑠 + 𝑎2 𝑠 2 + ⋯ + 𝑎𝑘 𝑠 𝑘
if a∈ [𝑎− , 𝑎+ ] , what will be the bounds of
𝑓 𝑠 ∈ [𝑓− , 𝑓+ ]
Analog Circuits Design Automation
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Kharitonov Theorem
 Read the paper “Performance Robustness Analysis of
VLSI Circuits with Process Variations Based on
Kharitonov’s Theorem”.
Analog Circuits Design Automation
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