EE142 Lecture23

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Amin Arbabian

Jan M. Rabaey

Lecture 24

Oscillators:

Steady-State Analysis

EE142 – Fall 2010

Nov. 23rd, 2010

University of California, Berkeley

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Review

Analyzed a multi-pole system with feedback,

derived oscillation conditions

Feedback view of oscillators, condition for

oscillation (gain and phase)

Today we will cover steady-state conditions for

oscillation and look at amplitude limiting

mechanisms….

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Review: LC Oscillator

AC

Small-Signal AC

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Small Signal Equivalent Circuit

With Loading

Loop Gain:

@ Resonance

𝐴𝑙 =𝑔𝑚𝑅

𝑛

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Closed Loop Transfer Function

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Closed Loop Gain vs Al

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Magnitude of the Poles

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Root Locus

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Role of Loop Gain

A

2

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Steady-State Analysis

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Steady-State Waveforms

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Steady State Equations

The input waveform is a scaled version of the output

This implies that:

Or that the loop gain in steady-state is unity and the

phase of the loop gain is zero degrees (an exact multiple

of 2π)

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Large Signal Gm

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Large Signal Gm (2)

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Large Signal Gm (3)

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Stability (Intuition)

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Intuition

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BJT Oscillator Design Procedure

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Design (2)

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Common Base Oscillator

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Colpitts Oscillator

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Colpitts with Bias

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Colpitts Family

If we remove the explicit ground connection on the

oscillator, we have the template for a generic oscillator.

Will come back to this later on (one-port view)

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Common-Emitter and Common-Collector…

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Pierce Oscillator

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Pierce Oscillator with Bias

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Common-Collector Oscillator

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Clapp Oscillator

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Negative Resistance Perspective

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Oscillator Stability

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Negative Resistance LC Oscillator

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Oscillation Condition