amplitude modulation early radio ee 442 spring 2017 · am modulation -- radio 4 baseband versus...

AM Modulation -- Radio 1

Amplitude Modulation – Early Radio EE 442 – Spring 2017

D. B. Estreich

http://www.technologyuk.net/telecommunications/telecom_principles/amplitude_modulation.shtml

LO audio baseband mf f f

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http://www.technologyuk.net/telecommunications/telecom_principles/amplitude_modulation.shtml

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Modulation Options

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwierOqgufHKAhUE02MKHcWFDi8QjRwIBw&url=http://www.slideshare.net/darshilshah940098/frequency-modulation-and-its-application&psig=AFQjCNHxejwF-RZ4XIjRnoziyjkHYMZ8PQ&ust=1455339757427298


Amplitude Modulation Illustrated

Radio Carrier fC

Audio tone fm

Amplitude Modulated

Signal

fC >> fm


Baseband versus Carrier-Based Communication

Baseband communication is the transmission of a message as generated.

Carrier communication requires the modulation of a message onto a carrier signal to transmit it over a different frequency band. We will use modulators or mixers to do the frequency translation.

(Note: “Pulse modulated” signals, such as PAM, PWM, PPM, PCM and DM are actually baseband digital signal coding (and not the result of frequency conversion).

Use of Sinusoidal Carriers: With a sine waveform there are 3 parameter s which we can “modulate” to carry a message on a carrier – they are the amplitude, frequency and phase of the sinusoid.

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Amplitude modulation (AM) is a modulation technique in which the amplitude of a high frequency sinusoidal carrier (a radio frequency carrier at frequency fC) is varied in direct proportion to a modulating baseband signal, m(t). The modulating signal contains the intended message, data or information – sometimes consisting of audio, as in radio broadcasting, or two-way radio communications as in cell phone conversations.

The high frequency carrier is modulated by combining it with the modulating signal, m(t), using a multiplier or mixer.

Amplitude Modulation (Verbal) Definition


Amplitude Modulation in Pictures

100 kHz carrier modulated by a 5kHz audio tone

100 kHz carrier modulated by an audio signal

(frequencies up to 4 kHz)

5 kHz Audio tone

Tone modulated AM signal

Baseband Voice modulated AM signal

Frequency Domain Time Domain

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjImoeZ5OnKAhVU92MKHTiwAUIQjRwIBw&url=http://jsantell.github.io/dsp-with-web-audio-presentation/&psig=AFQjCNE1gfPosQ2BtZJgpCxIONf7aDr4Vg&ust=1455076043850539


Example: Voice Signal – 300 Hz to 3400 Hz Baseband

time

amp

litu

de

m(t)

Symbol m(t) represents the source (baseband) message signal.

Time Domain

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Frequency Domain

Voice Band for Telephone Communication

Voice Channel 0 Hz – 4 kHz

Voice Bandwidth 300 Hz – 3.4 kHz

f 0 Hz 300 Hz 3.4 kHz 4 kHz 7 kHz

PSTN


3,400 Hz

Speech signal

Speech spectra

Representative Voice Spectrum for Human Speech

For the telephone AT&T determined many years ago that speech could be easily recognized when the lowest frequencies and frequencies above 3.4 kilohertz were cutoff.

Waveform as received from a microphone converting acoustic energy into electrical energy.

Fast Fourier transform of the above speech waveform showing energy over frequency from 0 Hz to 10 kHz.


A crystal radio receiver, also called a crystal set or cat's whisker receiver, is a very simple radio receiver, popular in the early days of radio. It needs no other power source but that received solely from the power of radio waves received by a wire antenna. It gets its name from its most important component, known as a crystal detector, originally made from a piece of crystalline mineral such as galena. This component is now called a diode.

Early AM Crystal Radio Receiver (The Bare Minimum)

Note: 1N34A is a germanium diode

Earphones

LC Tuned Circuit Selects Signal

Demodulator

Electrical to Acoustic

Transducer

C

11 AM Modulation -- Radio

Foxhole Radio (from World war I)

http://bizarrelabs.com/foxhole.htm

Ground

Coil – 120 turns of wire

Cold water pipe

Safety pin Razor blade

Earphones

“Earth” = Ground

Needle point

Demodulator

http://bizarrelabs.com/foxhole.htm


Diagram from 1922 showing the circuit of a crystal radio. This common circuit did not use a tuning capacitor, but used the capacitance of the coil and the antenna to form a “tuned circuit” with the coil.

Galena (lead sulfide) was probably the most common crystal used in cat's whisker detectors.

Crystal Radio Receiver from 1922

Sliding contact

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AM Radio Kits in the 1950’s

http://onetuberadio.com/2015/01/06/1956-boys-life-conelrad-receiver/










http://boycott-wisconsin.info/wp-content/uploads/2011/02/crystal-radio.jpg


AM Radio in the 21st Century

Parameter Value or Range

AM Broadcast Band 535 kHz to 1700 kHz

Channel Bandwidth 10 kHz

Channel Spacing 10 kHz

Carrier Stability 20 Hz about carrier fC

Maximum Broadcast Power 50 kW

Number of USA AM Stations 4,728 AM stations


Double-Sideband AM Modulation

( )m t

( )m t

( )m t

( )M f

( )M f

t

f

BB

2B

t fCfCf

LSBLSB

USBUSB

( )cos(2 )Cm t f t

( )cos(2 )Cm t f t( )m t

cos(2 )

CarrierCf t

Lathi & Ding; Page 181

Modulator

Frequency-shifting property

Double-sideband

(modulating signal) (modulated signal)

1

( )cos(2 ) ( ) ( )2

C C Cm t f t M f f M f f


Double-Sideband AM Demodulation

2

12

1 12 4

Output of mixer is ( ) ( ) cos(2 )

( ) ( ) 1 cos(2 2 ) , taking FT gives

( ) ( ) ( 2 ) ( 2 )

C

C

C C

y t m t f t

y t m t f t

F y t M f M f f M f f

Square-law mixer

( )cos(2 )Cm t f t

cos(2 )Cf t

Carrier

Demodulator

( )y t

2 Cf2 Cf f

12 ( )m t

Spectrum of y(t) LP Filter

Lathi & Ding; pp. 181-182

Note: No carrier is present

M(f)


Degree of Modulation: Modulation Index

The amplitude modulation “modulation index” is a measure of the extent of amplitude

variation upon the carrier. The AM modulation index measures the amount by which the

modulated carrier’s amplitude varies relative to its un-modulated amplitude level.

When expressed as a percentage is the same as the “depth of modulation.” It can be

expressed as:

where A is the carrier signal’s amplitude, and

M is the modulation amplitude (peak change in the RF amplitude relative

to its un-modulated value).

Example: For an AM modulation index of 0.5, the modulation causes the signal to increase

by a factor of 0.5 and decrease to 0.5 of the un-modulated carriers signal’s level.

( ) ( ) cos(2 )Cy t A m t f t

Modulation IndexM

A

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AM Modulation Index Basics - Examples

50% Modulation

100% Modulation

150% Modulation

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Single-Tone DSB Modulation & Demodulation

( )M f

f

f

f

Single tone modulation is cos(2fmt)

mfmf

Modulating signal’s spectrum

C mf fC mf f( )C mf f ( )C mf f

2 Cf2 Cfmf mf

DSB Spectrum

Demodulated signal spectrum

12 ( )M f

USBUSB LSBLSB


Suppressed by low-pass filtering

12

( ) cos 2 2 cos 2 2C m C my t f f t f f t


Sideband and Carrier Power

In general an AM signal takes the form of

( ) cos( ) ( ) cos( )AM C Ct A t m t t

Carrier Sidebands

The carrier power PC is the mean-square value of Acos(ct), which is [A2/2]. The sideband power PS is the power contained in m(t)cos (ct).

2

21( )

2 2C S

AP and P m t

The power efficiency is defined to be

2

2 2

useful power ( )100%

total power ( )S

C S

P m t

P P A m t

2

2Single tone: ( ) cos ; ( )2

C

Am t A t m t

modulation index


Power in AM Signals in General

0

0

1 2 22 2

0

2 2

( ) ( ) cos( ) cos( ) ( )cos( )

Carrier power is

1cos ( )

2 2

1Signal power is , whereas the

2message power uses an "appropriate" interval,

1( ) ( )

C

AM C C C

C C

C

S m

t T

m

t

t A m t t A t m t t

AP A t dt

P P

P m t m t dtT


Categories of Amplitude Modulation

Baseband spectrum Conventional or Full AM Double-Sideband-Suppressed Carrier (DSB-SC) Single-Sideband /Upper Sideband SSB/USB Single-Sideband /Lower Sideband SSB/LSB

f

f

f

f

f


Frequency Translation In General – from fC to fI

Multiplying a modulated signal by a sinusoidal moves the frequency band to sum and difference frequencies.

Note: Super-heterodyning: c + I ; Sub-heterodyning: c - I

Example 4.2: We want to convert from frequency C to frequency I .

Figure 4.7 Example 4.2


( )g t( ) cos( )cm t t ( ) cos( )Im t t

2 cos ( )c I t

2 f

Input frequency c Output frequency I


Modulators (or Mixers) – Types of Modulators

1. Electronic multiplier modulators

2. Nonlinear component modulators

3. Switching modulators

Integrated circuits have made it easy to buy inexpensive multipliers operating to very high frequencies with power gain.

Almost any nonlinearity will work, but a very inexpensive but strongly nonlinear device is a diode. Transistors are also nonlinear and work well as modulators.

Switching is an easily attained function with diodes and transistors in electronic circuits – especially in integrated circuits..


Multipliers Used for Modulation

difference frequency

1

2

Let signals ( ) and ( ) be RF & LO sinusoidal inputs.

If ( ) cos( ) and ( ) cos( ), then

( ) ( ) ( ) cos( ) cos( )

( ) cos(( ) ) cos(( ) )

RF LO

RF RF LO LO LO

RF LO RF RF LO LO

RF LO RF LO RF LO

g t s t

g t A t s t B t

y t g t s t A t B t

y t A B t t

sum frequency

RF

IF Multiplier

LO ( ) ( ) ( )RF LOy t g t s t

( )RFg t

( )LOs t


Using Nonlinearity For Modulation

Vo = Vdc + G Vi + A Vi2 + B Vi

3 + • • •

fRF = 0.8 fLO = 1.0

LO

RF

LO - RF LO + RF

Y(f)

f

2LO

- R

F

3RF 3LO

2LO

+ R

F

2RF 2LO

1 2 3 0

2RF

– L

O

2RF

+ L

O

Device Vi Vo

Let Vi = ARF

cos RF

t + BLO

cos LO

t , then we get frequencies,

Vi RF

and LO

(linear)

Vi2 (

RF +

LO), (

RF -

LO), 2

RF & 2

LO (square law)

Vi3 (2

RF+

LO), (2

RF-

LO), (2

LO+

RF), (2

LO-

RF), 3

RF & 3

LO

. . . through third order . . .

Conclusion: Nonlinearity generates new frequencies.


A “hopelessly unsophisticated” mixer.

Tom Lee (Stanford University)

The unbalanced single-diode mixer his no isolation and no conversion gain.

Single-diode mixers have been used in many applications --

(1) Detectors for radar in WW II (2) Early UHF Television tuners (3) Early radio receiver detectors (4) mm-wave & sub-mm-wave

receivers

IF

RF + LO

Using Nonlinearity For Modulation and Demodulation

Filter

A diode will work.


Demodulation: Nonlinear Component Demodulator

Lathi & Ding Figure 4.10

Page 196

1 13 5

At rectified output, the AM signal is multiplied by ( ), thus the half-wave

rectified ( ) is

( ) ( ( ))cos( ) ( )

1 2( ( ))cos( ) (cos( ) (cos(3 ) (cos(5 ) ....

2

C

C C C C

rectified

rectified

w t

V t

V t A m t t w t

A m t t t t t

dc term Baseb

.

and

1( )A m t other termsX

DC shift (eliminates A term)

LPF

FT of pulse train


Demodulation: AM Envelope Detector Circuit

Two conditions must be met for an envelope

detector to work:

(1) Narrowband [meaning fc >> bandwidth of m(t)] (2) A + m(t) 0


“Envelope Detector”


Choosing the RC Time Constant for an Envelope Detector

Time constant RC is too short. t

t Time constant RC is too long.

1

Design criteria is 2 2 CB fRC


Generating m(t)cos(2fct) using Convolution

Fold, Shift & Multiply

f

f

From Convolution Theorem: (t)m(t) Cn( f ) M( f )

F

F

M( f )

Cn( f ) (t)

m(t)

Output Spectrum

LO

RF

( )cos(2 )Cm t f t


Switching Modulator – Generating m(t)cos(2fct)

Figure 4.4 from Lathi & Ding;

Page 186 Pulse train


Example: Diode Ring (Switching) Modulator

Figure 4.6 from Lathi & Ding;

Page 188

1 1

3 5

4cos(2 ) cos(3 2 cos(5 2C C Cf t f t f t

cos(2 )CA f t

( )cos(2 )CK m t f t( )m tiv

Diodes are switched on and off

Output: DSB-SC

Diodes are matched


Analysis of the Diode Ring Modulator

The diodes are driven hard so they switch abruptly between ON and OFF states. Diodes D1 and D2 and ON while diodes D3 and D4 are OFF, an vice versa. The diode action is equivalent to generating a square wave w(t) with period T0. We accomplish this by driving the diodes with a frequency of fC = 1/T0.

1 1

3 5

4( ) cos( ) cos(3 ) cos(5 )C C Cw t t t t

Multiplying the modulating signal m(t) with w(t) results in

1 1

3 5

4( ) ( ) ( )cos( ) ( )cos(3 ) ( )cos(5 )C C Cm t w t m t t m t t m t t

After BPF this is the term giving AM modulated signal


Assumption: Diodes act a perfect switches (switch states: On or Off) and are controlled by the RF carrier signal (also called local oscillator).

Circuit Diagram of Diode Ring Modulator

T1 T2

D1

D2

D3

D4

RF carrier signal

cos(ct)

m(t) DSB-SC:

( ) cos( )Cm t tModulating Signal

Output:

Redraw the ring modulator:

http://electronicspost.com/ring-modulator-for-the-double-sideband-suppressed-carrier-generation/




















DRM Operation on the Positive Half-Cycle of Carrier

T1 T2

D1

D2

m(t) = 0

cos(ct)

+

currents

These currents cancel in the

primary.

Diodes D3 & D4 are Off

Positive Half-Cycle:

Result: Diodes D1 and D2 are switched to conducting state.


DRM Operation on the Negative Half-Cycle of Carrier

T1 T2

D3

D4

m(t) = 0

cos(ct)

+

currents

These currents cancel in the

primary.

Diodes D1 & D2 are Off

Negative Half-Cycle:

Result: Diodes D3 and D4 are switched to conducting state.


DRM Operation With Modulating Signal Applied

With diodes D1 and D2 on, signal on secondary of T1 is applied to T2. Non-inverting output is the result.

T1 T2

D1

D2

+ _

+ _

+ _

+ _

+ _

+ cos(ct)

m(t)

+ _

+ m(t)

output

During the Positive Half-Cycle:


DRM Operation With Modulating Signal Applied

T1 T2

D3

D4

+ _

+ _

+ _

+ _

+ _

+ cos(ct)

m(t)

+ _

- m(t) output

With diodes D3 and D4 on, signal on secondary of T1 is applied to T2. Inverting output is the result.

During the Negative Half-Cycle:


Net Output of Transformer T2 is AM Signal

Output as it would most likely appear after BPF

t

1 2&D D on3 4&D D on

DSB-SC signal at primary of T2

m(t)

OUTPUT

LO rectangular waveform

t

Output is proportional to m(t) during the positive cycle, and proportional to –m(t) during the negative cycle.

Summary


http://electronicspost.com/wp-content/uploads/2015/12/DSB-SC-output-of-ring-modulator.png




















Double-Balanced Diode Ring Mixer

LO input RF Input

IF Output

All internal processing is a balanced circuit which gives improved isolation.

Wire-wound toroid

transformer

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Commercial Diode Ring Mixer (Mini-Circuits)

Mixer in surface- mount package

Ring of FET devices operated as nonlinear

resistances

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Demodulator: Gilbert Cell Double-Balanced Mixer

IF Output

RF Input

LO Input

Widely used in microwave bands.

m(t)

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Demodulation of DSB-SC Signals

Demodulation of a DSB-SC signal involves multiplication with the carrier signal – it is identical to modulation. Reference: Figure 4.1 in Lathi & Ding.

At the receiver, the incoming signal is multiplied by a local carrier of frequency and phase in synchronism with the incoming signal. The only difference between the modulator and demodulator lies in input signal and the output filter.

With an incoming signal with suppressed carrier , the receiver must generate a local carrier which is synchronous in phase with the incoming signal. These demodulators are called synchronous or coherent demodulators.

Example 4.3 in Lathi & Ding;

page 190.


Spectrum of Conventional AM (DSB with Carrier)

12 2

In conventional AM a carrier is transmitted.

Let ( ) ( ).

The AM signal is written as

( ) cos 2 ( )cos 2 ( ) cos 2

Taking the Fourier transform gives

( ) ( ) ( ) (

AM C C C

AM C C CA

m t M f

t A f t m t f t A m t f t

t M f f M f f f f

) ( )

where we require ( ) 0

Cf f

A m t

Baseband

Carrier

http://en.wikipedia.org/wiki/File:AM_spectrum.svg


Superheterodyne Receiver is Widely Used

AM radio receiver:

This is a very widely used topology in communication receivers.


Elenco AM/FM Dual-Radio Receiver Kit (Model AMFM108CK)

http://www.elenco.com/product/productdetails/radio_kits=MTc=/am--fm_radio_kit_(transistor)=NzE=

http://www.elenco.com/product/productdetails/radio_kits=MTc=/am--fm_radio_kit_(transistor)=NzE



https://www.fcc.gov/media/radio/broadcast-radio-links


Single Sideband (SSB)

DSB-SC is spectrally inefficient because it uses twice the bandwidth of the message. The message uses bandwidth B but broadcast bandwidth 2B.

The signal can be reconstructed from either the upper sideband (USB) or the lower sideband (LSB).

SSB transmits a bandpass filtered version of the modulated signal.

Upper & Lower Bands


Single Sideband (SSB)

Multiplication of a USB signal by cos(ct) shifts the spectrum to left and right.


Phase-Shift Method to Generate SSB

( ) ( )cos( ) ( )sin( )

where minus sign applies to USB

and plus sign applies to the LSB.

( ) is ( ) phase delayed by - /2

SSB C h C

h

t m t t m t t

m t m t

See next slide

f

2

2

( )h f


Note on Quadrature Phase-Shift (/2)

-/2

Step 1 – Start with cos(t); then change phase by -/2.

Step 2 – The point at -/2 is now moved to the origin.

cos(t)

sin(t)

-/2 -/2 -/2 -/2

cos(t) sin(t) -cos(t) -sin(t) cos(t)

Reference:


Review: Spectral Lines for Sine and Cosine Signals

Example of a 90o phase shift

cos(t)

sin(t)

Time domain Frequency domain

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Pulse Amplitude Modulation (PAM) – A Digital Signal

How is PAM in digital communication is similar to AM in analog communication?

We will see that modulation for analog is essentially identical To modulation in the digital communications.

1 0 0 1 0 1 0


Questions

?

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amplitude modulation early radio ee 442 spring 2017 · am modulation -- radio 4 baseband versus...

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