LECTURE 010 – INTRODUCTION TO FREQUENCY SYNTHESIZERS


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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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LECTURE 010 – INTRODUCTION TO FREQUENCY SYNTHESIZERS
(References: [1,5,9,10]) What is a Frequency Synthesizer? A frequency synthesizer is the means by which many discrete frequencies are generated from one or more fixed reference frequencies.
Control

f1

fo

f2

Frequency

f3

Synthesizer

fo

fN Fig010-01
• The reference frequencies are stable and spectrally pure frequency typically generated from a piezoelectric crystal.
• Modern frequency synthesizers must provide many discrete output frequency so that it is impractical to generate the frequencies by having a reference frequency for each desired output frequency.
• The control input determines the value of the frequency synthesizer output frequency, fo

ECE 6440 Frequency Synthesizers Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

© P.E. Allen - 2003 Page 010-2

Characterization of a Frequency Synthesizer

• Output frequency range - fmin ≤ fo ≤ fmax

• Frequency accuracy - fo ± ∆f (typically in % or parts per million, ppm)

• Frequency switching time –

Frequency

Tolerance

f2

• Frequency resolution (channel spacing)
Magnitude
• Spectral purity (noise) –

f1
Spectral impurity

Switching Time

Time
Fig010-02

fo

Frequency

Fig010-03

• Frequency stability as a function of time, temperature and power supply

Expressed as parts per million per influence (time, temperature or power supply)

Short term (drift) Long term (aging) • Spurious outputs –

Magnitude Spurs

Desired Frequency
Spurs

ECE 6440 Frequency Synthesizers

Fig010-04

Frequency

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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Reference Frequencies

Ideally, the reference frequency should be a single frequency independent of all possible influences. It is very difficult to achieve an output frequency with better characteristics than the reference frequency.

Resonators

The reference frequency can be generated using resonators. Resonator technologies include:

• Quarter-wave resonators – lossless 1/4 wave transmission line (at 3 GHz λ/4 = 1 inch)

Barium titanate gives Q = 20,000

• Quartz resonators – although the piezoelectric effect is smaller, quartz has exceptional mechanical and electrical stability. Q ≈ 104 to 106.

t

f ≈ 1670 t

Cm

Co

Lm

RS

5x108 RS ≈ fo or
5x108 RS ≈ fo N2

Illustration of Bulk Shear Mode

Crystal Symbol and Model Fig010-05 N = overtones

Co = parallel plate capacitance, Lm and Cm = mechanical energy storage, RS = losses

• Surface acoustic wave devices

Surface waves avoid the undesired nonlinear behavior of bulk waves (LiNbO3)

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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Frequency Translation – Mixers Mixers require nonlinear or time-varying elements in order to provide frequency translation. Mixer types: • Multiplication – the output has only the sum and difference of the two input frequencies. • Modulation – the output not only has the sum and differences of the two input
frequencies, but many other frequencies Mixer fundamentals:
Acosω1t Mixer A2B [cos(ω1-ω2)t + cos(ω1+ω2)t]

Bcosω2t

Fig010-06

• A lowpass filter is used to obtain the difference frequency and a highpass filter to obtain the sum frequency

AB • The mixer gain is given as 2

• A mixer is difficult to analyze because the output frequency is different from the input frequency.

Note: The signals into the mixer do not need to be sinusoidal.

ECE 6440 Frequency Synthesizers

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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Mixer Types

1.) Passive and active mixers

2.) Mixers are classified as whether the inputs are balanced (differential) or unbalanced (single-ended)
(1.) Single-ended - both ω1 and ω2 are single-ended (2.) ω1-Balanced - ω1 is balanced and ω1 is single-ended (3.) ω2 -Balanced - ω2 is balanced and ω1 is single-ended
(4.) Doubly-Balanced - Both the ω1 and ω2 are balanced

Comparison:

Mixer Type →
Characteristic
ω1/ω2 Isolation ω1/ω2 Isolation ω1 Harmonic Rejection ω2 Harmonic Rejection

SingleEnded
Poor Poor None None

ω1-

ω2-

Balanced Balanced

Good Poor Even All

Poor Good
All Even

DoublyBalanced
Good Good
All All

Single-tone Spurious Rejection

None

?

?

?

Two-tone 2nd-order product rejection No

No

Yes

Yes

ECE 6440 Frequency Synthesizers Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

© P.E. Allen - 2003 Page 010-6

Frequency Translation – Frequency Dividers 1.) Flip-Flop Dividers

DQ FF1 X
DQ

DQ FF2 Y
DQ

fout = f2in

CLK
fin CLK

Fig010-10

Quadrature outputs are available at X and Y.

Need to load each flip-flop identically to insure the delays are equal.

2.) Miller Divider

x(t) ω1 + -

ω1,3ω1 22
ω1 2

Lowpass Filter

ω1 2 y(t)
Fig010-11

If x(t) = A1cosω1t, then the signal going into the lowpass filter is given as,

ω1t

3ω1t

ω1t

A2cos

2

 

+ A2cos

2

→


y(t) = A2cos

2

 

The filter cutoff frequency, fc, should be 0.5f1< fc < 1.5f1.

ECE 6440 Frequency Synthesizers

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

Frequency Translation – Frequency Multipliers 1.) Full-wave rectifier.

vout

vout

vin

vin

t

2.) Phase locked loop.
f1 f1 = f3
N

t

Fig010-12

Acos(φ1 -φ2)

Lowpass Filter

VoltageControlled Oscillator

f3 = Nf1

÷N
Fig010-13

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ECE 6440 Frequency Synthesizers Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

© P.E. Allen - 2003 Page 010-8

Filters

Filters are used to discriminate against certain frequencies and to pass other frequencies.

Lowpass:

Magnitude

1

TPB

Input

Output

Bandpass:

Magnitude 1
TPB

fc Frequency BW
Input

Fig010-07
Output

Highpass:

Magnitude 1
TPB

fo Frequency

Fig010-08

Input

Output

ECE 6440 Frequency Synthesizers

fc

Frequency

Fig010-09

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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Techniques for Frequency Synthesis
1.) Incoherent Synthesis – A relatively few reference frequencies are combined to generate many frequencies.
2.) Coherent Synthesis – A single reference frequency is used to generate many output frequencies.
• Coherent Direct Synthesis – Frequency mixers, frequency dividers, and frequency multipliers are used to generate many output frequencies. This method is also called arithmetic synthesis.
• Coherent Direct Digital Synthesis – Digital accumulators, ROMs, and digital-analog converters are used to generate a discrete-time approximation to a sine wave.
• Coherent Indirect Synthesis – Voltage controlled oscillators, mixers, phase locked loops (PLLs), frequency multipliers, and frequency dividers generate an output that has a definite relationship to a reference frequency.

ECE 6440 Frequency Synthesizers Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

© P.E. Allen - 2003 Page 010-10

Incoherent Synthesis Example:
f3 = 5.009 MHz

Bandpass f2+f3 =

Bandpass f1+f2+f3 =

f3

Filter 12.069 MHz

Filter 62.169 MHz

12.0-12.099 f2 = 7.06 MHz MHz

62.0-62.999 f1 = 50.1 MHz MHz

5.000 MHz 5.001 MHz 5.002 MHz 5.003 MHz 5.004 MHz 5.005 MHz 5.006 MHz 5.007 MHz 5.008 MHz 5.009 MHz 7.00 MHz 7.01 MHz 7.02 MHz 7.03 MHz 7.04 MHz 7.05 MHz 7006 MHz 7.07 MHz 7.08 MHz 7.09 MHz 50.0 MHz 50.1 MHz 50.2 MHz 50.3 MHz 50.4 MHz 50.5 MHz 50.6 MHz 50.7 MHz 50.8 MHz 50.9 MHz

Fig010-14
• This synthesizer covers the frequency range of 62.000 to 62.999 MHz • Thirty reference frequencies (crystals) are used to generate 1000 frequencies • Minimizing spurious outputs generated in the mixers is important • At one time, this synthesizer had the advantage of lowest cost, but now indirect digital
PLL synthesizers are less expensive.

ECE 6440 Frequency Synthesizers

© P.E. Allen - 2003

Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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Coherent Direct Synthesis

Example:

500+(0-9)+(0-9)/10 MHz 50+(0-9)/10+(0-9)/100 MHz

500+(0-9) MHz 50+(0-9)/10 MHz

500+(0-9)+(0-9)/10

50MHz ÷10

+(0-9)/100 MHz

÷10

fout

450 MHz 451 MHz 452 MHz 453 MHz 454 MHz 455 MHz 456 MHz 457 MHz 458 MHz 459 MHz

Advantages: • The speed of switching is high,
typically ≤ 10µs • The frequency resolution can be made very
high without affecting switching speed
ECE 6440 Frequency Synthesizers

Fig010-15
Disadvantages: • Complex system is too expensive to
build • Large number of mixers increases the
likelihood of spurious outputs
© P.E. Allen - 2003

Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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Coherent Direct Digital Synthesis (DDS) DDS generates the signal in the digital domain and utilizes an A/D converter and filtering to reconstruct the waveform in the analog domain. Illustration of the DDS principle:
Simple digital synthesis of a sine wave using a counter with N counts-

fclk fout = 2N

Increasing the output frequency by sampling fewer points-
ECE 6440 Frequency Synthesizers

fclk fout(max) ≈ 2.5
© P.E. Allen - 2003

Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)
DDS – Continued DDS using an accumulator to vary the frequency:

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Operation: The counter is implemented as an accumulator where a parallel-in, parallel-out M-bit register drives an adder in a feedback loop. On every clock cycle,
XR(k) = YR(k-1) + P When the register overflows, part of P appears as an increment in the new value of YR,
XR(k) = YR(k-1) + P modulo 2M

ECE 6440 Frequency Synthesizers Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)
DDS – Continued Example of the previous DDS using an accumulator (M=3):

© P.E. Allen - 2003 Page 010-14

For P = 1, the register goes from 000 to 111. Clock period increments the output phase by 2π/8.

For P = 2, the accumulator overflows after 110 and every other sample is read from the ROM causing the output phase to change every 2π/4.

For P = 3, the accumulator output begins at 000 and overflows at 110,11, and 101 in the first, second, and third cycles, respectively.

For P = 4, four cycles of the sinusoid are generated by the Nyquist-rate sampling.

fCK ∴ fout = P 2M

fCK

fCK

→ fout(min) = P 2M and fout(max) = P 2

ECE 6440 Frequency Synthesizers

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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DDS – Continued Comments: • D/A converter will introduce phase noise • The DDS can be FM, PM or AM modulated • The DDS can generate arbitrary waveforms • The DDS is capable of fast switching between frequencies • The DDS will generate spurs because the quantization error period changes between
even and odd values of P. The spurs can be minimized to below 70dBc if the ROM is about 12 bits. • DDS avoids the use of an analog VCO and achieves low phase noise • DDS provides fine frequency steps (close channel spacing) • DDS can provide continuous-phase channel switching at the output, an important property in some modulation schemes • DDS allows direct modulation of the output signal in the digital domain • DDS is restricted to lower frequencies (≈100 MHz) to avoid high power consumption

ECE 6440 Frequency Synthesizers Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

© P.E. Allen - 2003 Page 010-16

Coherent Indirect Synthesis

Function of a frequency synthesizer is to generate a frequency fo from a reference frequency fref. Block diagram:

Reference

Phase Frequency

LPF

VCO

fo

Frequency fref

Detector (PFD)

fo/N

Divider

Components:

(1/N)

Fig. 010-16

Phase/frequency detector outputs a signal that is proportional to the difference between the frequency/phase of two input periodic signals.

The low-pass filter is use to reduce the phase noise and enhance the spectral purity of the output.

The voltage-controlled oscillator takes the filtered output of the PFD and generates an output frequency which is controlled by the applied voltage.

The divider scales the output frequency by a factor of N.

fo fref = N →

fo = Nfref

ECE 6440 Frequency Synthesizers

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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Coherent Indirect Synthesis – Continued This type of frequency synthesizer is probably the most popular approach today and is very compatible with integrated circuit technology. Comments: • Frequency step size is equal to fref. Thus, for small channel spacing, fref, is small which
makes N large. • Large N results in an increase in the in-band phase noise of the VCO signal by
20log(N). • fo = N·fref • The loop filter has a significant impact on the performance of the frequency synthesizer-
- The bandwidth of the LPF is generally 5-10 larger than the reference frequency - The lower the bandwidth of the LPF, the less the phase noise - The higher the bandwidth of the LPF, the faster the switching time

The components of the above frequency synthesizer will be studied in much more detail in this course. You could say that this is a course on phase-locked loops.

ECE 6440 Frequency Synthesizers Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

© P.E. Allen - 2003 Page 010-18

Coherent Indirect Synthesis – Continued A modification of the previous system to enhance tradeoffs.

fref

Reference

Divider M Phase Frequency LPF

VCO

fo

Frequency fref (1/M)

Detector (PFD)

fo/N

Divider (1/N)

Fig. 010-17

The output frequency is equal to,

fref fo

N

M = N → fo = M fref

This gives more flexibility in the choice of fref and the bandwidth of the LPF.

ECE 6440 Frequency Synthesizers

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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Combination of Techniques
Combining the various approaches offers performance that could not otherwise be achieved by a single approach or technique.
Example of a DDS plus a coherent indirect synthesizer:

Clock Accumulator

fref

PLL Synthesizer

PFD

LPF

VCO

Fig. 010-17

cosθ ROM DDS
DAC + LPF

÷N

fhigh

flow

fout = fhigh +flow

Comments:
• The loop bandwidth can be optimized for noise since the output frequency can be changed rapidly and in small intervals by changing the DDS frequency, flow.
• The technique suffers from a limited output frequency range due to the low value of flow.
• If the purity requirements are high, the DAC needs to have a large number of bits and will be power hungry.

ECE 6440 Frequency Synthesizers

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Lecture 010 – Introduction to Frequency Synthesizers (5/5/03)

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SUMMARY
• This course will focus on the analysis and design of frequency synthesizers implemented using both discrete and integrated circuit technology.
• The coherent indirect synthesis method (PLL approach) will be the primary type of frequency synthesizer considered.
• Course outline:
- Introduction
- Technology
- PLLs
° PFDs ° Filters ° VCOs ° Dividers
- Frequency synthesizers
- Clock and data recovery circuits
- Applications of frequency synthesizers

ECE 6440 Frequency Synthesizers

© P.E. Allen - 2003

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LECTURE 010 – INTRODUCTION TO FREQUENCY SYNTHESIZERS