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Politecnico di Torino - ICT School

Analog and Telecommunication Electronics

B4 – Sine signal generators

» Oscillator taxonomy» Feedback oscillators, gain control» NIC circuits, –gm oscillator» Tuning with Varicap

AY 2015-16

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Lesson B4: sine signal generators

• Oscillator taxonomy• Sine oscillator parameters• Positive feedback circuits• Gain control• NIC circuits, –gm oscillator• Tuning with Varicap• Quartz crystal oscillators

• Text references: – Elettronica per Telecom.: 1.2.4 Generatori sinusoidali– Design with Op Amp …: 10.1 Sine Wave Generators

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Oscillators: where?

Referenceoscillatorand VCO

I/Q signalgenerators

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Sine signal parameters

• Expected output: v(t) = V sen (ωt + θ)– Amplitude V– Frequency/angular frequency ω = 2π f– Phase θ

• Real circuits have nonlinearity & noise– Difficult to analyze in the time domain– Move to the frequency domain

– Spectral purity» Components at other frequencies (harmonics, spurs, …) » Output is not a sinewave distortion

– Phase noise: θ = θ(t)

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Spectrum and phase noise

fo 2fo 3fo

f

fo

v(t) = V sin (ωt + )

t

Peakvalue V

Period T = 1/f = 2/Phase

f

fxSpurious Phase noise

Spectralpurity

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Oscillator block diagram

• Feedback loop– Positive feedback

• Barkhausen criterion– Conditions for value and

phase of loop gain:

|A β| = 1arg(A β) = 0

– To get constant amplitude oscillations a signal travelling in the loop must keep constant amplitude and phase

– Usually A = A(x) and β = β(ω)» The task to get |A β| = 1 is achieved by A (the amplifier)

I

E

A

U+ D

+

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Loop gain condition

• Goal: |A β| = 1– In most circuits A = A(x); β = β(ω)

• Condition achieved through a gain control on A– Amplifier with gain compression (nonlinearity)

• Oscillation startup– At startup the loop gain |A β| must be > 1

• Amplitude stabilization– Gain decreases as signal amplitude increases– For high signal levels |A β| < 1

• The |A| = 1 condition is met only for a specific signal level

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Operating zone

Compression area

Steep gain changevs signal level x

A(x); |A(x) β(ω)| = 1

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Phase control

• The only element which (explicitly) causes phase rotation is the LC resonant circuit.

– The arg(A) = 0 condition occurs only at the resonant frequency fo of the LC circuit

– For a more detailed analysis also other reactive elements must be taken into account

ffo

Arg (Zc)

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LRC resonant circuits

• Parameters– Resonance angular

frequency: ωo

– damping: ξ

• Amplitude peakand slope of phase rotation depends from Q

– Q = 5– Q = 10– Q = 100

|z()|

o

arg(z())

Q

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Effect of Q

• Amplifier introduces additional phase shift• Total phase rotation must be 0• The frequency shift Δω required to get 0 total phase

rotation depends from Q.

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Single transistor CB oscillator

• Transistor amplifier + LC circuit– Load is a LC circuit– Positive feedback– Gain controlled

through the nonlinearity

Vr

A

VoD

+A

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Example 1: Colpitts oscillator

• Feedback with capacitive voltage divider

• β network;with ideal circuit:

– No loss– Phase rotation = 0

in the network

A

21

1

CCCvv or

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Example 2: Hartley oscillator

• Inductive feedback divider

– To get positivefeedback the amplifier configuration is common base (Gain > 0 from E to C)

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Example 3: Meissner oscillator

• Feedback through a transformer– Feedback voltage Vr towards Emitter or Base

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Example 4: differential circuit

• Q2 transistor is a CC stage, and isolates the LC group from Q1 emitter (Q2 bias network not shown)

• Reduced load on LC tuned circuit

• Higher Q

• Less harmonics

Q2

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Frequency error (Colpitts circuit)

A

• Ideal circuit– No loss– Phase rotation = 0

in the network

• Actual circuit:– Req in parallel

with LC– Capacive divider

loaded with 1/gm– Additional phase

rotation in

• Frequency errors

A Req

1/gm

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Problem B4-1: oscillator design

• Specs– Sine output– Vi level: 104 mVpeak– Ic = 0,2 mA– Total Req on LC circuit = 10 kohm

• Compute– Required β network divider ratio– Output level Vo– Actual Q for ωo = 10 MHz– Output spectrum – Actual load on feedback divider (Req)

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RLC resonant circuit

• LC tuned circuit with loss resistance R1

• Signals decay due to dissipation on R1

R1C

L

stimulus

response

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Negative transconductance oscillator

• LC tuned circuit with loss resistance R1

• Active circuit with -gm transconductance, connected in parallel to LC

• Gtot = 1/R1 - gm

– If:

gm = 1/R1

Gtot = 0Rtot

– constant amplitude oscillations

R1C

L

-gm

Active network

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Negative transconductance (–gm)

• An active circuit (with gain) is required to get the negative transconductance –gm

– Subject to nonlinearity, distortion, saturation, …

• At startup:– Small signal,

» High gm Rtot < 0» Signal is amplified

• Signal level regulation:– For increasing signal level

» gm, is reduced Rtot becomes positive losses!» Signal is attenuated

– Only stable condition: Rtot = 0

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NIC: Negative Impedance Converter

• Positive feedback circuit

• Zi = Vi/Ii = - Z/K

– Allows to get Zi < 0 (L from C, …)

– The Zi value depends from actual gain

– Nonlinearity and saturation make |Zi| decrease as the signal level increases

KR

A.O.

-

+

R

VI

VO

II

Z

Active network

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Impedance converter circuit

• Vo = (K + 1) Vi– WARNING: gain is K+1

• Across the impedance Z:

Vz = K Vi

• Ii = - K Vi/Z

• Vi/Ii = - Z/KKR

A.O.

-+

R

VIVO

II

Z

VZ

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Example of –gm circuit

• A negative differential Req appears between D1 and D2:

– Can be seen as a fully differential amplifier (input: G, output: D)

– Small signal:Req = - 2/gm

– Large signal:Req = - 2/Gm(x)

– Gm(x) decreases when the signal level (x) increases

VDD

S

D1

G

D2

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Differential circuits

• The –gm sine source is symmetric (differential)

• Benefits– Constant current sink from the power supply

» The current is deviated to either branch of the differential circuit» Less radiated noise and EMI

– No even harmonics(keeping differential signals)

– Reduced noise sensitivity» The useful signal is differential» Common mode signals are ignored

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Frequency control (VCO)

• Resonant frequency can be modified by changing L or C.

– Total C depends on a Varicap diode (see also VCO for PLL)– Need to isolate control voltage Vc from/to HF signal

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Real circuits and Q

• The resonant circuit Q depends on losses– Loss of L (series Rs) and C (parallel Rp)– The total resistive load on the LC group is the parallel of:

» Input resistance of the following stage» hOE or rD of transistor» Re referred to Vo

• To reduce losses (and raise Q)– Increase parallel Req

» Reactive network» Separation buffer between feedback and load » Use mechanical resonators (with high Q)» Use quartz oscillators

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Quartz oscillators

• Quartz is a piezoelectric material– Under mechanical stress generates electrical signals– When receives electrical signals modifies size and shape – The electric-mechanic energy conversion is very efficient at the

(mechanical) resonant frequency

• Quartz crystal = resonator with very high Q– Can be used to build precise and stable oscillators

» By replacing the LC group» With specific circuits (mainly squarewave generators)

• Other resonators use the same techniques (mechanic resonance)

– Ceramic filters, SAW, …

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Quartz crystal

Quartzthin plate(mechanicalresonator)

Metal coating

Contact toexternal pins

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Lesson B4: final test

• Which parameters describe (completely) a sine signal?

• Draw the block diagram of a single-transistor sine generator.

• How does a NIC work?

• Describe the operation of a NIC-based sine generator.

• Is it possible to build a fixed-amplitude sine generator with fully linear devices?

• Discuss the benefits of differential configurations for signal generators.

• Which are the benefits of quartz oscillators?