01/04/2011 - 1 ATLCE - B4 - © 2010 DDC
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
01/04/2011 - 2 ATLCE - B4 - © 2010 DDC
Lesson B4: sine signal generators
• Oscillator taxonomy• Sine oscillator parameters• Positive feedback circuits• Gain control• NIC circuits, –gm oscillator• Tuning with Varicap
• Text reference: sect. 1.2
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Oscillators: where?
Referenceoscillatorand VCO
I/Q signalgenerators
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Sine signal parameters
• v(t) = V sen (ωt + θ)– Amplitude V– Frequency/angular frequency ω = 2 f– Phase θ
• Spectral parameters– Spectral purity
» Components at other frequencies (harmonics, spurs, …)
– Phase noise» θ = θ(t)
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Spectrum and phase noise
fo 2fo 3fo
f
fo
v(t) = V sen (ωt + )
tPeak value V
Period T = 1/f = 2/Phase
f
fx
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Oscillator block diagram
• Feedback loop– Positive feedback
• Barkhausen criterion– Conditions for
value and phase of loop gain:
|A | = 1phase(A ) = 0
– A signal traveling in the loop keeps constant amplitude and phase
– That corresponds to constant amplitude oscillations.
I
E
A
U+ D
+
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Loop gain condition
• Must be achieved through a gain control– Amplifier with gain compression (nonlinearity)
• Oscillation startup– At startup the loop gain muste be > 1
• Amplitude stabilization– Gain decreases as signal amplitude increases
• The |A| = 1 condition is met only for a well defined signal level
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Operating zone
Compression area
Steep gain changevs signal level x
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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
• The frequency error Δω, for a given phase error, depends from Q.
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Single transistor 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
• Ideal circuit– No loss– Phase rotation = 0
in the network
A
21
1
CCCvv or
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Colpitts oscillator: frequency error
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 error
A Req
1/gm
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Example 2: Hartley oscillator
• Inductive feedback divider
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Example 3: Meissner oscillator
• Feedback through a transformer– Feedback voltage Vr towards Emitter or Base
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Test: 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
– Ifgm = - 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» 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
• On 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 Req appears between D1 and D2:
– 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 is symmetric (differential)
• Benefits– Costant 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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Example of differential circuit
• Q2 transistor isolates the LC group from Q1 emitter(Q2 bias network not shown)
Q2
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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?
