ELCT 1003 - GUC · Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering...

ELCT 1003: High Speed Electronic Circuit

Lecture 3: Oscillators (Continued)

Dr. Mohamed Abd El Ghany,

Department of Electronics and Electrical Engineering

[email protected]

LC Oscillators

2 Dr. Mohamed Abd el Ghany


LC oscillators have the advantage of having relatively small reactive

elements. They exhibit higher Q than RC oscillators, but they are difficult

to tune over a wide range.

LC Oscillators

Colpitts Oscillators Hartley Oscillators

Colpitts Oscillators



213

21

CCL

CCw

osc

2

1

1

2

C

C

R

R

For an oscillator, Aβ=1

Hartley Oscillators



)(

1

213LLC

wosc

1

2

1

2

L

L

R

R

For an oscillator, Aβ=1

Crystal Oscillators



Crystal

reactance

Inductive

Capacitive

Because of their excellent frequency stability, quartz crystals are commonly

used to control the frequency of oscillation. If the inductor L of the Colpitts

oscillator is changed to a crystal, the oscillator is called a crystal oscillators.

Crystal oscillators are commonly used in digital signal processing.

Crystal Oscillators

Dr. Mohamed Abd el Ghany


The quality factor Q of the crystal can be as

high as several hundred thousand.

L has a large value (as high as hundreds of

henries)

Rs can be as high as a few hundred

thousand ohms.

Cp >> Cs, Cp (parallel capacitance) of order of

pF.

Properties of the crystal:

6

Crystal Oscillators



Since Q is very high in the typical

quartz crystal, we may neglect Rs.

The crystal impedance is given by:

)1

//()1

()(ps

sCsCsLsz

)

)(

1

1

)(1

()(2

2

ps

ps

s

p

CC

CCL

s

LCs

sCsz

))(1

()(22

22

p

s

pww

ww

wCjjwz

s

s

LCw

1

LCC

CCw

ps

ps

p

Colipitts Oscillator Using a Crystal



s

osc

LCw

1

21

21

111

11)(1

1

CCC

CCCC

LCw

p

ps

s

osc

Cp >> Cs

Ring Oscillators



Odd Number of Inversions

If a cascade of M gain stages with an odd number of

inversions is placed in a feedback loop, the circuit oscillates

with a period equal to 2MTd, where Td is the delay of each

stage . The oscillation can be viewed as occurring at the

frequency for which the total phase shift is zero and the loop

gain is unity.

Ring Oscillators



Example: Differential Ring Oscillator

A differential ring oscillator is shown.

a) Find the frequency of oscillation in Hz if R=1KΩ and C= 1pF

b) What value of gm is required for oscillation assuming all stages are identical?

c) What is the maximum positive and maximum negative voltage swing at the

drains if Iss= 1mA and VDD=2V?

Ring Oscillators



Example: continued

a) The voltage transfer function of a single stage is,

Solution

11)(

)(

1

s

Rg

sRC

Rg

sV

sVmm

in

out where sRC sec10 9

1

The phase shift around the loop will be 360o or 0o. Therefore, the oscillation

frequency can be found as,

2)(tan31

1

oscw MHz

RCf

osc67.275

2

732.1

Ring Oscillators



Example: continued

b) The magnitude of the loop gain at the oscillation frequency is given as

Solution

1

1

3

2

RCw

Rg

osc

m 231732.11 2 Rgm

msR

gm

22

Vv 2max

c) Vmax = VDD = 2V and vmin = VDD - IssR= 2 -1 = 1V

Vv 1min

Phase Noise



As other analog circuits, oscillators are susceptible to noise. Noise injected

into an oscillator by its constituent devices or by external means may

influence both the frequency and the amplitude of the output signal. In most

cases, the disturbance in the amplitude is negligible, and only the random

deviation of the frequency is considered.

In RF application, phase noise is usually characterized in the frequency

domain. for an ideal sinusoidal oscillator operating at wc, the spectrum

assumes the shape of an impulse, whereas for an actual oscillator, the

septum exhibits “skirts” around the carrier frequency.

Actual Oscillator Ideal Oscillator

Phase Noise



To quantify phase noise, we consider a unit bandwidth at an offset △w with

respect to wc, calculate the noise power in this bandwidth, and divide the

results by the carrier power.

Phase Noise



Effect of phase noise in RF Communications

If the Local Oscillator (LO) output contains phase noise, both

downconverted and upconverted signals are corrupted.

The carrier signal for

the transmit path

The carrier signal for

the receiver path

Phase Noise



Effect of phase noise in RF Communications : (continued )

The signal of interest is convolved with an impulse and thus translated

to a lower (and a higher) frequency with no change in the shape

Down conversion by

an ideal oscillator

Phase Noise




In reality, the wanted signal may be accompanied by a large interferer in an

adjacent channel, and the local oscillator exhibits finite phase noise. When the

two signal are mixed with the LO output, the downconverted band consists of two

overlapping spectra, with the wanted signal suffering from significant noise due to

the tail of the interferer. This effect is called “reciprocal mixing”

Reciprocal mixing

Phase Noise




Suppose a noiseless receiver is to detect a weak signal at w2 while a powerful,

nearby transmitter generates a signal at w1 with substantial phase noise. Then,

the wanted signal is corrupted by the phase noise tail of the transmitter.

Effect of phase noise in

transmitters

Phase Noise




The total noise power introduced by the interferer in the desired channel is equal to

Example: in the figure, where the wanted channel is

30 KHz wide and 60 dB below an unwanted channel

60 KHz away. How low should the phase noise of the

unwanted channel 60 KHz offset be so that the SNR in

the desired channel exceeds 15 dB?

Solution

dffSpH

L

f

f ntotn)(

, Where Sn(f) denotes the phase noise profile of the unwanted

channel and fL and fH are the lower and upper ends of the

desired channel, respectively.

For simplicity, we assume sn(f) is constant in

this bandwidth and equal to So, )(

, LHototnffSp

Phase Noise




Solution: (continued)

)(LHo

sig

ffS

PSNR

)log(1015)/log(10LHsigo

ffdBPS

dBPPsig

60log10log10int

Pint is the interferer power

dBffdBPSLHo

60)log(1015)/log(10int

When integrated in a 30 KHz band, the phase noise must not exceed -70

dBc

The phase noise must not exceed -120dBc/Hz at 60 kHz offset.

Q of an Oscillator



The definition of Q that proves especially useful in oscillators is

shown in the following figure

The Q is defined as

dw

dwQ o

2

Where is the phase of the open-

loop transfer function

)(w

ELCT 1003 - GUC · Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering...

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