10.PDF

Contents

10.1 The Mechanism of Mixers and Mixing

10.1.1 What is a Mixer?

10.1.2 Putting Multiplication to Work

10.2 Mixers and Amplitude Modulation

10.2.1 Overmodulation

10.2.2 Using AM to Send Morse Code

10.2.3 The Many Faces of Amplitude

Modulation

10.2.4 Mixers and AM Demodulation

10.3 Mixers and Angle Modulation

10.3.1 Angle Modulation Sidebands

10.3.2 Angle Modulators

10.3.3 Mixers and Angle Demodulation

10.4 Putting Mixers, Modulators and Demodulators

10.5 A Survey of Common Mixer Types

10.5.1 Gain-Controlled Analog Amplifiers

As Mixers

10.5.2 Switching Mixers

10.5.3 The Diode Double-Balanced Mixer:

A Basic Building Block

10.5.4 Active Mixers — Transistors as

Switching Elements

10.5.5 The Tayloe Mixer

10.5.6 The NE602/SA602/SA612:

A Popular Gilbert Cell Mixer

10.5.7 An MC-1496P Balanced Modulator

10.5.8 An Experimental High-Performance

Mixer

10.6 References and Bibliography

to Work

10.4.1 Dynamic Range: Compression,

Intermodulation and More

10.4.2 Intercept Point

Chapter 10 —

CD-ROM Content

Supplemental Articles

• “Modern Receiver Mixers for

High Dynamic Range” by Doug

DeMaw, W1FB (SK) and George

Collins, KC1V

• “Performance Capability Of Active

Mixers” by Dr Ulrich Rohde, N1UL

Chapter 10

Mixers, Modulators and

Demodulators

Amateur Radio textbooks have traditionally handled mixers separately from modulators

and demodulators, and modulators separately from demodulators. This chapter examines

mixers, modulators and demodulators together because the job they do is essentially the

same. Modulators and demodulators translate information into radio form and back again;

mixers translate one frequency to others and back again. All of these translation processes

can be thought of as forms of frequency translation or frequency shifting — the function

traditionally ascribed to mixers. We’ll therefore begin our investigation by examining what

a mixer is (and isn’t), and what a mixer does.

At base, radio communication involves

translating information into radio form,

letting it travel for a time as a radio sig-

nal, and translating it back again. Trans-

lating information into radio form entails

the process we call modulation, and

demodulation is its reverse. One way or

another, every transmitter used for radio

communication, from the simplest to

the most complex, includes a means of

modulation; one way or another, every

receiver used for radio communication,

from the simplest to the most complex,

includes a means of demodulation.

Modulation involves varying one or

both of a radio signal’s basic charac-

teristics — amplitude and frequency

(or phase) — to convey information. A

circuit, stage or piece of hardware that

modulates is called a modulator.

Demodulation involves reconstruct-

ing the transmitted information from the

changing characteristic(s) of a modulat-

ed radio wave. A circuit, stage or piece

of hardware that demodulates is called a

demodulator.

Many radio transmitters, receivers and

transceivers also contain mixers — cir-

cuits, stages or pieces of hardware that

combine two or more signals to produce

additional signals at sums of and differ-

ences between the original frequencies.

This chapter, by David Newkirk,

W9VES, and Rick Karlquist, N6RK,

examines mixers, modulators and

demodulators. Related information may

be found in the Modulation chapter,

and in the chapters on Receivers and

Transmitters . Quadrature modulation

implemented with an I/Q modulator, one

that uses in-phase (I) and quadrature

(Q) modulating signals to generate the

0° and 90° components of the RF signal,

is covered in the chapters on Modula-

tion and DSP and Software Radio

Design .

10.1 The Mechanism of Mixers

and Mixing

10.1.1 What is a Mixer?

Mixer is a traditional radio term for a circuit that shifts one signal’s frequency up or down

by combining it with another signal. The word mixer is also used to refer to a device used to

blend multiple audio inputs together for recording, broadcast or sound reinforcement. These

two mixer types differ in one very important way: A radio mixer makes new frequencies out

of the frequencies put into it, and an audio mixer does not.

MIXING VERSUS ADDING

Radio mixers might be more accurately called “frequency mixers” to distinguish them

from devices such as “microphone mixers,” which are really just signal combiners , summers

or adders . In their most basic, ideal forms, both devices have two inputs and one output.

The combiner simply adds the instantaneous voltages of the two signals together to produce

the output at each point in time ( Fig 10.1 ). The mixer, on the other hand, multiplies the in-

stantaneous voltages of the two signals together to produce its output signal from instant to

instant ( Fig 10.2 ). Comparing the output spectra of the combiner and mixer, we see that the

combiner’s output contains only the frequencies of the two inputs, and nothing else, while the

mixer’s output contains new frequencies. Because it combines one energy with another, this

process is sometimes called heterodyning , from the Greek words for other and power . The

sidebar, “Mixer Math: Mixing as Multiplication,” describes this process mathematically.

The key principle of a radio mixer is that in mixing multiple signal voltages together,

it adds and subtracts their frequencies to produce new frequencies. (In the field of signal

processing, this process, multiplication in the time domain, is recognized as equivalent to the

process of convolution in the frequency domain. Those interested in this alternative approach

to describing the generation of new frequencies through mixing can find more information

about it in the many textbooks available on this subject.)

The difference between the mixer we’ve been describing and any mixer, modulator or

demodulator that you’ll ever use is that it’s ideal. We put in two signals and got just two

signals out. Real mixers, modulators and demodulators, on the other hand, also produce

distortion products that make their output spectra “dirtier” or “less clean,” as well as putting

out some energy at input-signal frequencies and their harmonics. Much of the art and sci-

ence of making good use of multiplication in mixing, modulation and demodulation goes

Mixers, Modulators and Demodulators

10.1

Fig 10.1 — Adding or summing two sine waves of different frequencies (f1 and f2) combines their amplitudes without affecting

their frequencies. Viewed with an oscilloscope (a real-time graph of amplitude versus time), adding two signals appears as a

simple superimposition of one signal on the other. Viewed with a spectrum analyzer (a real-time graph of signal amplitude versus

frequency), adding two signals just sums their spectra. The signals merely coexist on a single cable or wire. All frequencies that

go into the adder come out of the adder, and no new signals are generated. Drawing B, a block diagram of a summing circuit,

emphasizes the stage’s mathematical operation rather than showing circuit components. Drawing C shows a simple summing

circuit, such as might be used to combine signals from two microphones. In audio work, a circuit like this is often called a mixer —

but it does not perform the same function as an RF mixer.

Fig 10.2 — Multiplying two sine waves of different frequencies produces a new output spectrum. Viewed with an oscilloscope, the

result of multiplying two signals is a composite wave that seems to have little in common with its components. A spectrum-analyzer

view of the same wave reveals why: The original signals disappear entirely and are replaced by two new signals — at the sum and

difference of the original signals’ frequencies. Drawing B diagrams a multiplier, known in radio work as a mixer. The X emphasizes

the stage’s mathematical operation. (The circled X is only one of several symbols you may see used to represent mixers in block

diagrams, as Fig 10.3 explains.) Drawing C shows a very simple multiplier circuit. The diode, D, does the mixing. Because this circuit

does other mathematical functions and adds them to the sum and difference products, its output is more complex than f1 + f2 and

f1 – f2, but these can be extracted from the output by iltering.

10.2

Chapter 10

Mixer Math: Mixing as Multiplication

Since a mixer works by means of multiplication, a bit of math can show us how

they work. To begin with, we need to represent the two signals we’ll mix, A and B,

mathematically. Signal A’s instantaneous amplitude equals

(1)

A sin2 f t

in which A is peak amplitude, f is frequency, and t is time. Likewise, B’s instanta-

neous amplitude equals

A sin2 f t

(2)

Since our goal is to show that multiplying two signals generates sum and differ-

ence frequencies, we can simplify these signal deinitions by assuming that the peak

amplitude of each is 1. The equation for Signal A then becomes

a(t) Asin (2 f t)

π a

(3)

and the equation for Signal B becomes

(4)

b(t) Bsin (2 f t)

π b

Each of these equations represents a sine wave and includes a subscript letter to

help us keep track of where the signals go.

Merely combining Signal A and Signal B by letting them travel on the same wire

develops nothing new:

Fig 10.3 — We commonly symbolize

mixers with a circled X (A) out of tradition,

but other standards sometimes prevail (B,

C and D). Although the converter/changer

symbol (D) can conceivably be used to

indicate frequency changing through

mixing, the three-terminal symbols are

arguably better for this job because they

convey the idea of two signal sources

resulting in a new frequency. ( IEC

stands for International Electrotechnical

Commission .)

(5)

a(t) b(t) Asin (2 f t) Bsin (2 f t)

As simple as equation 5 may seem, we include it to highlight the fact that multiply-

ing two signals is a quite different story. From trigonometry, we know that multiplying

the sines of two variables can be expanded according to the relationship

[

]

sin x sin y

cos (x

− −

y) cos (x

(6)

Conveniently, Signals A and B are both sinusoidal, so we can use equation 6 to

determine what happens when we multiply Signal A by Signal B. In our case, x =

2 π f a t and y = 2 π f b t, so plugging them into equation 6 gives us

how to get rid of it in a balanced modula-

tor ?” A transmitter enthusiast may ask “Why

didn’t you mention sidebands and how we

conserve spectrum space and power by get-

ting rid of one and putting all of our power

into the other?” A student of radio receivers,

on the other hand, expects any discussion of

the same underlying multiplication issues to

touch on the topics of LO feedthrough , mixer

balance ( single or double ?), image rejection

and so on.

You likely expect this book to spend some

time talking to you about these things, so it

will. But this radio-amateur-oriented discus-

sion of mixers, modulators and demodulators

will take a look at their common underly-

ing mechanism before turning you loose on

practical mixer, modulator and demodulator

circuits. Then you’ll be able to tell the for-

est from the trees. Fig 10.3 shows the block

symbol for a traditional mixer along with

several IEC symbols for other functions mix-

ers may perform.

It turns out that the mechanism underly-

ing multiplication, mixing, modulation and

demodulation is a pretty straightforward

thing: Any circuit structure that nonlinearly

distorts ac waveforms acts as a multiplier to

some degree.

(

[

]

)

(

[

]

)

(7)

a(t) b(t)

cos 2

−

cos 2

Now we see two momentous results: a sine wave at the frequency difference

between Signal A and Signal B 2 π (f a – f b )t, and a sine wave at the frequency sum

of Signal A and Signal B 2 π (f a + f b )t. (The products are cosine waves, but since

equivalent sine and cosine waves differ only by a phase shift of 90°, both are called

sine waves by convention.)

This is the basic process by which we translate information into radio form and

translate it back again. If we want to transmit a 1-kHz audio tone by radio, we can

feed it into one of our mixer’s inputs and feed an RF signal — say, 5995 kHz — into

the mixer’s other input. The result is two radio signals: one at 5994 kHz (5995 – 1)

and another at 5996 kHz (5995 + 1). We have achieved modulation.

Converting these two radio signals back to audio is just as straightforward. All we

do is feed them into one input of another mixer, and feed a 5995-kHz signal into the

mixer’s other input. Result: a 1-kHz tone. We have achieved demodulation; we have

communicated by radio.

into minimizing these unwanted multiplica-

tion products (or their effects) and making

multipliers do their frequency translations

as efficiently as possible.

tion isn’t made any easier by the fact that

traditional terms applied to a given multipli-

cation approach and its products may vary

with their application. If, for instance, you’re

familiar with standard textbook approaches

to mixers, modulators and demodulators, you

may be wondering why we didn’t begin by

working out the math involved by examining

amplitude modulation , also known as AM .

“Why not tell them about the carrier and

10.1.2 Putting Multiplication

to Work

Piecing together a coherent picture of how

multiplication works in radio communica-

Mixers, Modulators and Demodulators

10.3

NONLINEAR DISTORTION?

The phrase nonlinear distortion sounds

redundant, but isn’t. Distortion, an externally

imposed change in a waveform, can be linear;

that is, it can occur independently of signal

amplitude. Consider a radio receiver front-

end filter that passes only signals between 6

and 8 MHz. It does this by linearly distorting

the single complex waveform corresponding

to the wide RF spectrum present at the radio’s

antenna terminals, reducing the amplitudes

of frequency components below 6 MHz and

above 8 MHz relative to those between 6 and

8 MHz. (Considering multiple signals on a

wire as one complex waveform is just as val-

id, and sometimes handier, than considering

them as separate signals. In this case, it’s a bit

easier to think of distortion as something that

happens to a waveform rather than something

that happens to separate signals relative to

each other. It would be just as valid — and

certainly more in keeping with the consensus

view — to say merely that the filter attenu-

ates signals at frequencies below 6 MHz and

above 8 MHz.) The filter’s output waveform

certainly differs from its input waveform; the

waveform has been distorted. But because

this distortion occurs independently of signal

level or polarity, the distortion is linear. No

new frequency components are created; only

the amplitude relationships among the wave’s

existing frequency components are altered.

This is amplitude or frequency distortion, and

all filters do it or they wouldn’t be filters.

Phase or delay distortion , also linear,

causes a complex signal’s various compo-

nent frequencies to be delayed by different

amounts of time, depending on their frequen-

cy but independently of their amplitude. No

new frequency components occur, and ampli-

tude relationships among existing frequency

components are not altered. Phase distortion

occurs to some degree in all real filters.

The waveform of a non-sinusoidal signal

can be changed by passing it through a circuit

that has only linear distortion, but only non-

linear distortion can change the waveform of

a simple sine wave. It can also produce an out-

put signal whose output waveform changes as

a function of the input amplitude, something

not possible with linear distortion. Nonlinear

circuits often distort excessively with overly

strong signals, but the distortion can be a

complex function of the input level.

Nonlinear distortion may take the form of

harmonic distortion , in which integer multi-

ples of input frequencies occur, or intermodu-

lation distortion (IMD) , in which different

components multiply to make new ones.

Any departure from absolute linearity re-

sults in some form of nonlinear distortion,

and this distortion can work for us or against

us. Any amplifier, including a so-called lin-

ear amplifier, distorts nonlinearly to some

degree; any device or circuit that distorts

and f 3 , and the sum and difference of f 2 and

f 3 , but not the sum and difference of f 1 and

f 2 . Fig 10.4 shows that feeding two signals

into one input of a mixer results in the same

output as if f 1 and f 2 are each first mixed with

f 3 in two separate mixers, and the outputs

of these mixers are combined. This shows

that a mixer, even though constructed with

nonlinearly distorting components, actually

behaves as a linear frequency shifter. Tradi-

tionally, we refer to this process as mixing and

to its outputs as mixing products , but we may

also call it frequency conversion , referring to

a device or circuit that does it as a converter ,

and to its outputs as conversion products . If

a mixer produces an output frequency that is

higher than the input frequency, it is called an

upconverter; if the output frequency is lower

than the input, a downconverter.

Real mixers, however, at best act only as

reasonably linear frequency shifters, generat-

ing some unwanted IMD products — spuri-

ous signals, or spurs — as they go. Receivers

are especially sensitive to unwanted mixer

IMD because the signal-level spread over

which they must operate without generating

unwanted IMD is often 90 dB or more, and

includes infinitesimally weak signals in its

span. In a receiver, IMD products so tiny that

you’d never notice them in a transmitted sig-

nal can easily obliterate weak signals. This is

why receiver designers apply so much effort

to achieving “high dynamic range.”

The degree to which a given mixer, modula-

tor or demodulator circuit produces unwanted

IMD is often the reason why we use it, or don’t

use it, instead of another circuit that does its

wanted-IMD job as well or even better.

Fig 10.4 — Feeding two signals into

one input of a mixer results in the same

output as if f 1 and f 2 are each irst mixed

with f 3 in two separate mixers, and the

outputs of these mixers are combined.

nonlinearly can work as a mixer, modula-

tor, demodulator or frequency multiplier. An

amplifier optimized for linear operation will

nonetheless mix, but inefficiently; an ampli-

fier biased for nonlinear amplification may

be practically linear over a given tiny por-

tion of its input-signal range. The trick is to

use careful design and component selection

to maximize nonlinear distortion when we

want it (as in a mixer), and minimize it when

we don’t. Once we’ve decided to maximize

nonlinear distortion, the trick is to minimize

the distortion products we don’t want, and

maximize the products we want.

OTHER MIXER OUTPUTS

In addition to desired sum-and-difference

products and unwanted IMD products, real

mixers also put out some energy at their input

frequencies. Some mixer implementations

may suppress these outputs — that is, reduce

one or both of their input signals by a factor

of 100 to 1,000,000, or 20 to 60 dB. This is

good because it helps keep input signals at

the desired mixer-output sum or difference

frequency from showing up at the IF termi-

nal — an effect reflected in a receiver’s IF

rejection specification. Some mixer types,

especially those used in the vacuum-tube era,

suppress their input-signal outputs very little

or not at all.

Input-signal suppression is part of an

overall picture called port-to-port isolation .

Mixer input and output connections are tra-

ditionally called ports . By tradition, the port

to which we apply the shifting signal is the

local-oscillator (LO) port. By convention,

the signal or signals to be frequency-shifted

are applied to the RF (radio frequency) port,

and the frequency-shifted (product) signal

or signals emerge at the IF (intermediate

KEEPING UNWANTED DISTORTION

PRODUCTS DOWN

Ideally, a mixer multiplies the signal at one

of its inputs by the signal at its other input, but

does not multiply a signal at the same input

by itself, or multiple signals at the same input

by themselves or by each other. (Multiplying

a signal by itself — squaring it — generates

harmonic distortion [specifically, second-

harmonic distortion] by adding the signal’s

frequency to itself per equation 7. Simultane-

ously squaring two or more signals generates

simultaneous harmonic and intermodulation

distortion, as we’ll see later when we explore

how a diode demodulates AM.)

Consider what happens when a mixer must

handle signals at two different frequencies

(we’ll call them f 1 and f 2 ) applied to its first

input, and a signal at a third frequency (f 3 )

applied to its other input. Ideally, a mixer

multiplies f 1 by f 3 and f 2 by f 3 , but does not

multiply f 1 and f 2 by each other . This pro-

duces output at the sum and difference of f 1

10.4

Chapter 10

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: