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Mixed-Signal-Electronics

PD Dr.-Ing. Stephan Henzler

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Switched Capacitor Circuits

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Chapter 3

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Resistor Realizations in MOS Technologies: Poly-Resistor

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Sheet resistance:

200-400Ω□ (metal

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Resistor Realizations in MOS Technologies: Diffusion Resistor

Sheet resistance: 50-150Ω□ 

Highly variable resistance (up to +/- 20%)

Parasitic diode

High parasitic capacitances

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Resistor Realizations in MOS Technologies

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Sheet resistance:

 Poly: 200-400Ω□ 

 Diffusion: 50 -150Ω□  Metal:

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Effect of Resistor between two Nodes

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continuous time point-of-view discrete time point-of-view

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Switched Capacitor Resistor Emulation 1

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Switched Capacitor Resistor Emulation 2

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Resistor Equivalents

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Non-Overlapping Multiphase Clocking

both clocks active at the same time

would cause short circuit currents

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Parameter Variations in SC Circuits 1

What is the variation of a RC time constant?

i.e. the relative error of the time constant is equal to the sum of

the relative error of the resistance and the capacitance

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Parameter Variations in SC Circuits 2

What happens for the switched-capacitor equivalent?

i.e. the relative error of the time constant is equal to the relative

error of a capacitance ratio

 very small if matching is considered in layout

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Implementation of Integrated Capacitors

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 Alternative Capacitor Implementation

Junction capacitance

 – Parasitic diode  leakage

 – Voltage and temperature dependent

MOS capacitance

 – MOS transistor in accumulation or inversion

 –  Alternatively: gate over diffusion

 – Strongly non-linear

 – Very high capacitance/area

 – God for decoupling Vertical parallel plate capacitor

 – Matrix of wires exploiting vertical and lateral capacitance

 – Ref. next slide

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Vertical Parallel Plate Capacitor

Kim, VLSI Symposium 2003

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Li it ti f SC E i l

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Limitations of SC-Equivalence

Continuous Time RC-Low-Pass

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Limitations of SC-Equivalence

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S1 and S2 are

closed alternately

Li it ti f SC E i l

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Limitations of SC-Equivalence

Switched Capacitor Low-Pass

z-Transformation:

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Li it ti f SC E i l

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Limitations of SC-Equivalence

Switched Capacitor Equivalence

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Switched Capacitor Integrators

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Switched Capacitor Integrators

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A l i f S it h d C it Ci it

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 Analysis of Switched-Capacitor Circuits

 – SC-Cookbook – 

Mark polarity of all capacitors (arbitrarily)Do not change this polarity during the analysis

Draw equivalent circuit for each clock phase

Charge balance analysis for full cycle

 – assume steady state conditions for each time step

 – compute ∆Q that occurs during phase transitions 

z-transformation

Calculate transfer function

Evaluate transfer function on unit circle of z-plane

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Spectral Analysis

z-Transformation

 Approximation on unit circle

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Spectral Analysis (cont.)

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A l i f S it h d C it Ci it

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 Analysis of Switched-Capacitor Circuits

 – SC-Cookbook – 

Mark polarity of all capacitors (arbitrarily)Do not change this polarity during the analysis

Draw equivalent circuit for each clock phase

Charge balance analysis for full cycle

 – assume steady state conditions for each time step

 – compute ∆Q that occurs during phase transitions 

z-transformation

Calculate transfer function

Evaluate transfer function on unit circle of z-plane

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Impact of Parasitic Capacitances

Cp1||C1  direct impact on transfer behavior  

Cp2 shorted no impact  

Cp3 shorted between GND and VGND  

Cp4 at opamp output  negligible impact  

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1

1

2

11

1 

 z 

 z 

C 

C C  z  H 

  p

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 Alternative Integrator Architectures

Sign of transfer function can be changed by switching the

control signal of the switches.

Less sensitive to parasitic capacitances

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Switched Capacitor Amplifier

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Switched Capacitor Amplifier: Impact of Offset

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SC Amplifier: Output Signal

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opamp offset

Switched Capacitor Amplifier

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Switched Capacitor Amplifier

(without output reset)