1

Balanced mixers

A multiplier circuit, where the output amplitude is proportional to the product of two input signals, can be used as a balanced mixer

V1 = sinω1t

V2 = sinω2t

Vo = V1 x V2 = 0.5 x [cos(ω1t - ω2t) – cos(ω1t + ω2t)]

2

Applications of balanced mixers

AM Modulation

Data (…01101001…)

Carrier

Output Signal

AM de-modulation

Signal input

Local oscillator

Output Signal

Filter

3

Detection schemes

Signal input

Output Signal

Filter

Self-mixing homodyne detection

Homodyne and heterodyne detection

One example of heterodyne detection (See P. Hu’s paper)

4

Phase detector using mixer

Signal input

The DC output depends on the phase of the two paths

The output is related to the phase difference of the two signals of the same frequency

5

Comparison of oscillators

LC oscillators: susceptible to vibration, temperature changes, aging…

Crystal oscillators: Good stability, but narrow tuning range

Frequency synthesizers: Good stability and tunability, preferred method of frequency generation in most modern transmitters and receivers

6

Central component of frequency synthesizer - phase locked loop

Phase detector

LPF Amp VCO

OutputInput

The output always tracks the input frequency

Besides frequency tracking, one immediate application is clock recovery

7

Capture range: The range over which the reference frequency can be varied and still achieve phase lock

Lock range: The total frequency range within which lock, once achieved, can be maintained

Example 2.8

How to characterize a PLL

8

Phase detector

Integrator

10GHz VCO

RZ data in

Clock out

PLL output RF spectrum

-80

-60

-40

-20

0

-5.00E+05 -3.00E+05 -1.00E+05 1.00E+05 3.00E+05 5.00E+05

Frequency offset (Hz)

Po

wer

(d

Bm

)

A 10-G PLL

9

Simple frequency synthesizer

Phase detector

LPF Amp VCO

OutputInput

/ N divider

FM and AM channel spacing

Example 2.9

10

A practical example – 29M to 4.8M synchronization circuit

200

10

MAV11100

Clk ResetD1D0

74F163Counter

29MHzpulsein

5V

MAV11

D Q_

Clk Q74F74

D Flip-Flop

4.84 MTTL

Output

7K

4.7u150 150

4.7u

15V

MRV901

4K

1K

29MHz / 6 circuit

29MHz amplification, digitization and frequency division circuit (All capacitors are 0.1uF).

11

2K

10K

10K 100K

+6V 5

8

UPG506B 14GHz divide by 8 Prescalar

2.2V Zener

1000UF

10GHVCO

Splitter

+15V To 10G laser

1.5K

1.5K

+17V

10 dBm 2-10 dBm

1

UPB1502 1.25GHz divide by 128 Prescalar

2

3

4

8

7

6

5

-15~0 dBm

74F86 XOR gate

4.84 MHz TTL Input

74F74 f/2

4.8M to 10G synchronization circuit

12

Spectrum of 4.827MHz square signal wave. Span: 500Hz, RB: 30Hz. 

Spectrum of 4.827MHz square signal wave. Span: 500Hz, RB: 30Hz.

Experimental results

13

Pre-scaling

Phase detector

LPF Amp VCO

OutputInput

Fixed /M

Programmable /N

Fixed /Q

Example 2.10

14

Frequency translation

The movement of a block of frequencies is called a frequency translation

Two configurations:

Synthesizer with frequency shifting

Synthesizer with mixer in the loop

Example 2.11

15

Transmission lines

Coaxial cables (solid dielectric, air dielectric)

Parallel line cables (television twin-lead, open-wire line, shielded twin-lead)

Twisted pair cable – used as transmission lines for relatively low frequencies

16

Two models of short transmission line section

Balanced line

Unbalanced line

G

R L

C

At DC, the inductance and the capacitor have no effect

17

Step and pulse response of lines

Vi

Transmission line

Since the line has capacitance to be charged, the initial current will not be zero

18

Characteristic impedance: the ratio of voltage to current through the transmission line with a step signal

Concept of matched line

Characteristic impedance Z0 = sqrt[(R + jwL) / (G + jwC)]

Many lines approach Z0 = sqrt(L/C)

Example 14.1, 14.2

Characteristic impedance

19

Reflection (step input)

Open end scenario

Short end scenario

Pulse input…

Energy does not disappear at the open end, since there is nothing capable of dissipating energy

20

Some definitions

Γ = Vr/Vi: reflection efficient

Γ = (ZL – Z0) / (ZL + Z0)

Meaning of the above equation:

1. To have zero reflection, ZL has to be equal to Z0

2. By measuring Γ, ZL can be derived to probe the internal characteristic of the load

Example 14.13

21

An example to know the internal parameters of a tunable laser

Lp

Cp

Rp

Cs

Rsub

D

Parasitics PN junction

Rs

SourceTransmission

line

S11

S11 = (ZL – Z0) / (ZL + Z0)

Parameters Reflector biased at 10 mA

Is (A) 1.79E10-5

q 4.47

Rp (ohm) 0.1

Rs (ohm) 0.1

Rsub (ohm) 1.0

Cp (pF) 4.58

Cs (pF) 355

Lp (nH) 21.4

22

Voltage driver is better than current driver

Current response Optical response

Y. Su et al, IEEE PTL Sept. 2004

23

Wave propagation

In a matched line, a sine wave moves down the line and disappear into the load. Such a signal is called a traveling wave

Example 14.5

RF Phase shifter

24

Standing waves

The interaction between the incident and reflected waves causes what appears to be a stationary pattern of waves on the line, which are called standing waves

SWR = Vmax/Vmin

For a matched line, the SWR = 1

25

Relation between Γ and SWR

SWR = (1+ |Γ|) / ( 1 - |Γ|)

If ZL >Z0,

SWR = Z0 / ZL

Example 14.6

26

27