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Amin ArbabianJan M. Rabaey

Lecture 5:Resonance Two-Ports

EE142 – Fall 2010Introduction

Sept. 9th, 2010

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Announcements

HW2 Posted, due Thurs. Sept. 16th, 330pm before class in EE142 drop box

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Overview

Last Lecture– Resonance circuits, series RLC “Tank”

– Passive amplification

– Quality factor

This Lecture– More on Resonant circuits

– Bandwidth of tuned circuits

– Tuned amplifiers

– Introduction to two ports

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Source of Resonance

What makes the circuit resonate?– Reactive components cancel

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+ + --vL vC

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Back to Transfer Function

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Canonical Form

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Root Locus

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Selectivity

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Selectivity

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Bandwidth and Q

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Parallel RLC Circuit

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Circuit Duality

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Duality

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Circuit Duality

Basic Circuit Theory, Desoer and Kuh

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Q and Phase Response

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Phase Response

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Transfer Function

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Parallel RLC Transfer Function

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Parallel Resonance

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Tuned Amplifier

Parallel RLC load results in a tuned amplifier. – The impedance of the load

is selective.

How is gain related to Q?

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Series-Shunt Transformation

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Transformer

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Tank Dominated by Inductor Q

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Inductance Value for Tuned Amplifier

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Other Advantages of Tuned Amplifier

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Cascode Tuned Amplifier

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Tuned Amplifier Bandwidth

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What are the Limits?

To win some of the bandwidth back requires other techniques, such as shunt peaking and distributed amplifiers. Other techniques (some invented here at Berkeley) can also help out.

But can we tune out parasitics and design amplifiers operating at arbitrarily high frequency?

Based on the simple analysis thus far, it seems that for any given frequency, no matter how high, we can simply absorb the parasitic capacitance of the amplifier with an appropriately small inductor (say a short section of transmission line) and thus realize an amplifier at an arbitrary frequency. This is of course ludicrous and we’ll re-examine this question in future lecture.

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TWO PORT NETWORKS

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Introduction to Two Port Networks

Design problems often need abstraction– Concerned with external behavior (@ “Terminals”)

– A Black-Box view of the component

– Replace by characteristic parameters

When physical circuit models start to fail– High frequency operation

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Introduction (2)

A port is defined as a terminal pair where the current entering one terminal is equal and opposite to the current exiting the second terminal.

Any circuit with four terminals can be analyzed as a two-port if it is free of independent sources and the current condition is met at each terminal pair.

All the complexity of the two-port is captured by four complex numbers (which are in general frequency dependent).

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Two Port Network Representations

Various equivalentways of relating the terminal parameters

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Conversion Table

W.S.Harwin, University of Reading

All matrices in the same row are equivalent

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Example: Transformer

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Coupled Inductors

Z Matrix