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Politecnico di Torino - ICT School

Analog and Telecommunication Electronics

B3 - Using nonlinearity

» Tuned amplifier » Frequency multiplier » Gain compressor » Adding feedback

AY 2015-16

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Lesson B3: using nonlinearity

• Reducing the effects of nonlinearity– Tuned amplifiers– Large signal gain Gm(x)– Re feedback– Gain stabilization

• Exploiting nonlinearity– Dynamic compressors– Frequency multipliers

• Text reference:– Elettronica per Telecom.: sect. 1.2 Transistori fuori linearità

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Nonlinearity: fight or exploit ?

• We get: – Distortion– Harmonics – Variable gain

• Remove harmonics: tuned circuits

• Keep harmonics: frequency multipliers

• Stabilize the gain: negative feedback

• Use gain variation: compressor, VGA, mixers

• Sine oscillators:– Use gain change to get |Aβ| = 1

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Limit the effects of nonlinearity

• Negative feedback– OpAmp or OpAmp-like with feedback– Add feedback to transistor amplifiers

(Emitter resistance)» Reduce actual signal amplitude on the nonlinear element (pn

junction)

• Same effect for any frequency

• Suitable for wideband amplifiers

• No problem for fully integrated circuits

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Reduce harmonics and distorsion

• Tuned circuit at the output: ZC(ω)– Gain: |AV| ZC(ω)/ZE(ω)

• Suitable for narrowband amplifiers– Can attenuate the harmonics (and other unwanted signals)

– TX output stage (PA)» Remove unwanted components

– RX front end amplifiers (LNA)» Remove unwanted (outband) signals» Remove noise

• Fully integrated amplifiers low L C values– Tuned circuis feasible for F > K x 100 MHz

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Tuned amplifiers

LNA (low noise amplifier)

IF amplif.(tuned amplifiers)

PA (power amplifier)

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fi2 = fi1 – fO2

Dual-conversion heterodyne receiver

Input RF filterFirst IF:High easy image removal Second IF (IF2)Low Simple channel filter

Tuning by shifting O1 (or O2)

WidebandLNA + filter

X

O1

DEM.Va

IF1 filter +Amplif.

f

fa fO1fi1 = fa – fO1

X

O2IF2 filter +Amplif.

ffO2fi1 fi1b

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LRC tuned circuits

• Resonance: o

• Damping:

• Quality factor: Q = 1/2 • Attenuation:

k1kQX

k

X

logω

|z()|

Q

O kO

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Tuned amplifiers

• IC depends only on VBE

IC

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Tuned amplifiers

• VO depends on IC (VBE) and ZC ()

In this example O = I

VO

IC

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Output spectrum

• Harmonic contents of collector current Ic– IC current spectrum

depends only on Vi amplitude

• Effects of LC on Vu– Vu spectrum depends also from Zc, that is the resonator Q– add (in dB) the level caused by nonlinearity with resonant circuit

attenuation X– X depends from

frequency offset and quality factor Q

k

1kZ

Z kQXi

i

I

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Examples: fixed Q, variable Vi

Harmonic content of Ic depends only on input signal levelThe tuned circuit Q factor modifies the harmonic content of Vu

|Zc|, Q = 200(fixed)

Ic(ω)For Vi 5 …200 mVp

Vu(ω)

Vi = 5mV Vi = 20mV Vi = 200mV

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Examples: variable Q, fixed Vi

Harmonic content of Ic depends only on input signal levelThe tuned circuit Q factor modifies the harmonic content of Vu

|Zc|, Q = 50, 200, 500

Ic(ω) for Vi = 200 mVp(fixed)

Vu(ω)

Q = 50 Q = 200 Q = 500

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Example: tuned amplifier design

• Functional parameters:– Input signal level– Gain– Spectral purity– Power and efficiency

• Circuit parameters– Collector current IC (= IE = I)– Resonant circuit Q

• Exercise B3-a– From signal level and Q, compute output spectrum– Compute the Q required to get a given spectral purity

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Lesson A4: how to use nonlinearity

• Reducing the effects of nonlinearity– Tuned amplifiers– Gain stabilization

• Exploiting nonlinearity– Dynamic compressors– Frequency multipliers

• Sine oscillators– Positive feedback amplifiers– Negative transconductance

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Large-signal gain

• Input signal

• Small signal (linear model)

• Large signal (slide B2-12) (only fundamental component)

• Introducing large signal transconductance: Gm(x)(gain for the fundamental)

i Tv (t) x V cos t

o C m i

1m

T 0

v (t) R G (x)v (t)

I (x)IG (x) 2x V I (x)

1o C i

T 0

I (x)Iv (t) R 2 v (t)x V I (x)

o C m iv (t) R g v (t)

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Gm(x)

• Very low-level input signal (x 0)

– Gm(x)/gm = 1 (small signal, linear)

• As input level increases,

– Gm (x)/gm decreases (less gain)

• Steep slope for x = 3 … 6… compression

Small signal

Compression

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Verification for small signal

• Low level input signal: x 0

• Fundamental component

• Same results as from small signal (linear) analysis

I0(x) = 1 o C m i

1m

T 0

v (t) R G (x)v (t)

I (x)IG (x) 2x V I (x)

-

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Gain change

• As signal amplitude increases, the gain decreases:compressionSmall signal

High compression

Output saturation: ≈ squarewave output high distortion:

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Signal level for 1 dB compression

• From Gm(x) curve:

Gm(x) = gm - 1 dB = 0,89 gm

x ≈ 1; Vi ≈ 26 mV

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Compressing amplifiers: where?

• RF signal have variable, unknown amplitude– In FM receivers, AM is noise compression OK– In AM receivers, AM is the useful signal NO compression

• FM IF amplifiers: remove AM (fast): – Compressing amplifiers

• AM IF amplifiers: keep AM, but …– Received signal amplitude changes (fading, slow)

– Need for AGC» Compensate slow changes» Ignore fast changes (modulation !)

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Gain compression: example

• Functional parameters:– Input level– Compression coefficient

• Circuit parameter– Resonant circuit Q

• Test B.3-a– Analysis of a compressing amplifier

» From input levels, compute AM index at the output

minVmaxVminVmaxV

m

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Gain stabilization: emitter feedback

• Input signal VI partitioned among VBE and RE

– Voltage drop on RE : RE iC– VBE = Vi – iC RE

VBE = Vi – Gm(x’) VBE RE

– x’ = VBE/VT ; x = Vi/VT

– x’ is defined by an equation without closed form solution:

• Can be solved only with successive approximation

-

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Gain with emitter feedback

-

i BET T

BE i C E C m BE

BE i m BE E

iBE

m E

m CO m C BE i

m E

m E

1

1

1

V Vx ; x'V VV V i R ; i G (x')V

V V G (x')V RVV

G (x')R

G (x')RV G (x')R V VG (x')R

xx'G (x')R

Can be solved only with successive approximation

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Frequency multipliers

• Input signal: sinewave at ωi

• Vi harmonics in the collectrocurrent IC

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Frequency multipliers

• Input signal at ωi

• Nonlinearity brings Vi harmonics in the IC (b)

• A tuned circuit isolates the planned harmonic (c)

– Different attenuationfor 2 ωi and 4 ωi

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Frequency multiplier: example

• Functional parameters (specs):– Multiplication factor N– Output spectral purity

• Circuit parameter (design)– Input amplitude– Tuned circuit Q

• Design problems– Design a frequency multiplier x N, from the input level and

spectral purity specifications– Compute the minimum Q required for the tuned circuit

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Frequency multiplier: test B.3-c

• Test B.3-c– An AM signal with Vmax = 260 mV; Vmin = 26 mV goes through

a BJT amplifier (without emitter feedback).– Find the modulation index Mo at the output

• Solution– x = 10 1– Gm/gm = 0,190 0,893 (slide B3-17)– Vo = - Rc Gm (x) Vi – M = (Vmax – Vmin)/(Vmax + Vmin);

» Input signal: Mi = 0,8 » Output signal:

Mo = (10 Gm (10) – Gm (1))/(10 Gm (10) + Gm (1)) = 0,36

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Lesson B3: final test

• Which are the techniques usable to reduce harmonic content and distortion in amplifiers?

• Is there any difference between the spectral content of collector current and of collector voltage in a tuned amplifier?

• Define large signal transconductance.

• Which parameters describe a RLC tuned circuit?

• Where can be useful a compressing amplifier?

• Describe how the Emitter DC voltage depends on input signal level.

• Define the 1-dB compression point.

• List the parameters which define the spectral purity of a frequency multiplier.