Electricity is a difficult substance to appreciate with the human senses. About the only way you get a feeling for it is to moisten the tongue and apply it between the terminals of a 9 volt battery. Of course, you get more idea if you are unfortunate enough or foolish enough to touch a live mains cable… providing that you survive to describe the experience.

Here are some electrical quantities and their SI units and symbols.

• Electric charge (coulombs), q or Q
• Volume charge density (coulombs per cubic meter) rho
• Surface charge density (coulombs per square meter) sigma
• Linear charge density (coulombs per meter) lambda
• Electrostatic potential (volts) phi
• Electric field (volts per meter) E
• Electric induction D = epsilon.E (coulombs per square meter) D
• Electric current (amps or coulombs per second) I
• Electric current density (amps per square meter) J
• Magnetic field H (amps per meter or amp turns per meter) H
• Magnetic field B = mu.H (tesla) B
• Magnetic vector potential (tesla meters) A
• Capacitance (coulombs per volt, or Farads) C
• Inductance (volts-seconds per amp, or Henries) L
• Permittivity (Farads per meter) epsilon
• Permeability (Henries per meter) mu
• Velocity of light in vacuum (meters per second) c

A loose description.

Electric fields form lines which are trajectories along which a very small free charge would travel in the absence of a magnetic field in the same place.

Magnetic fields form lines along which little bar magnets “dipoles” or iron filings would align.

The flow of charge constitutes a current. Charge is neither created or destroyed, so if in a region there is a changing charge (with time) then there must be current flow in or out of that region. Currents often travel along electric field line directions and generate magnetic fields.

In regions of constant charge density, all currents flow in closed loops. If the current loop does not close then there must be accumulation of charge which varies with time.

All magnetic fields B form closed loops. Loops of B are linked with loops of current density (J) or displacement current density ((d/dt)D).

Electric field lines either begin or end on charges or else they too form closed loops.

In a radiating situation, the currents, charges, fields, and potentials are all time varying. If one assumes a sinusoidal variation with time having angular frequency omega, then a general radiation problem can be solved by Fourier superposition of the solutions at different values of the angular frequency omega. Fortunately in most practical situations the fractional bandwidth occupied by the signal is rather small and so the properties of the radiating structure do not vary very much across the band of signal frequencies.

Mathematical presentation of Maxwell’s Equations

There are four of Maxwell’s Equations plus a charge continuity equation. You need to study your favorite vector differential calculus book to learn about the divergence (div), curl (curl), and gradient (grad). Roughly, the gradient represents the “slope” of a scalar field along the direction of maximum change, and the gradient is a vector. The divergence represents the flow out of a small volume, per unit volume, and is a scalar. The curl represents the rotation of a field around a point; for a magnetic field forming closed loops it is the limit of the size of the field times the perimeter of the loop divided by the area of the loop, as the loop shrinks to nothing. The curl is a vector as it has an associated axis of circulation or direction in space.

Here are the four Maxwell’s equations and the continuity equation.

• div D = rho
• div B = 0
• curl E = – (d/dt)B
• curl H = (d/dt)D + J
  and the continuity equation for charge….
• div J + (d/dt)rho = 0

Let us go through these…

• Lines of D, electric induction, are proportional to the electric field and “diverge” away from a region containing charge density rho. If there is a surface charge sigma (coulombs per square meter) then close to the charge sheet is an electric induction field D = sigma.
• Lines of B never diverge from anything, and form closed loops.
• Electric field lines which form closed loops, encircle a changing magnetic field. Lenz’s law applies; the electric field if it drove a current would do so in such a way as to reduce the changing magnetic field within the loop. Electric field lines which do not form closed loops begin and end on charge, as we have seen from the first equation.
• Magnetic field lines H form loops which encircle both conduction current density J, and also “displacement current density” (d/dt)D which is generated by time-varying electric fields. Maxwell’s great achievement was to realize that the term in (d/dt)D was necessary; if you consider a capacitor with plates very close together, then if the displacement current term did not generate magnetic field loops there would be an unphysical discontinuity in the magnetic fields around the capacitor plates as you passed alternating current through the capacitor.
• The current density J flowing out of a region (“diverging”) must result in a decrease of charge within the region.

Sources of fields

Currents and charges give rise to the fields and are called “sources”. More directly, the potentials can be calculated from the source charge and current distributions and the fields are then derived from the potentials.

In an electrostatics situation the electric field E is given just by

E = -grad(phi) which begins and ends on charges.

However, if there are changing magnetic fields there is an additional contribution to the electric field forming the closed loops which circulate around the changing magnetic field lines.

The magnetic vector potential A may be used to find the magnetic field B by the relation (which is a definition of A)

B = curl(A)

To define A completely we have to specify its divergence as well as its curl, and possibly an additive constant also. If we do this according to what is known as the “Lorentz Gauge” then the electric field may be calculated from

E = -(d/dt)A – grad(phi)

Part of the source of electric field is from the magnetic vector potential A and part from the scalar potential phi.

If we know the potentials A and phi completely for all time and space we can calculate the fields E and B.

A little more detailed mathematics (see the text of your choice) shows that the conduction currents J give rise to the magnetic vector potential A, and the source charges rho give rise to the scalar potential phi. Because there is a maximum velocity of propagation c=3E8 meters per second, the potentials A and phi at a distance r meters from the source cannot follow changes in the source distributions until a time r/c seconds later. These potentials are known as the “retarded potentials”.

Considering the equation

E = -grad(phi) – (d/dt)A

we observe that in the far field the potentials A and phi fall off as 1/r where r is the distance from the sources. However, applying the gradient operator to phi puts in a further dependence of 1/r to the contribution -grad(phi). Thus the electric field E due to the charges in the source falls off as 1/(r^2) and can be neglected at large r compared to the electric field contribution -(d/dt)A which falls off as 1/r.

Thus, for far field calculations it is true to say that only the source currents on the antenna structure need be considered.

For time-harmonic currents, since the charge continuity equation links the current density J to the source charge density rho, the potential phi may be expressed in terms of the vector potential A, and so there is no loss of generality in considering the far-fields as being entirely due to source currents plus any pre-existing electromagnetic propagating waves.

It is very easy to conduct a gedankenexperiment to show that, for near field scenarios, the conduction currents on the source structures are not sufficient to use as a basis for field calculations.

Consider an open ended waveguide carrying a TE10 waveguide mode. Let us assume that the waveguide is very large in transverse dimensions compared to a wavelength. Now consider a point on the axis of the waveguide, beyond the plane at which the waveguide stops, along the z-direction. Let us assume that this point is closer to the point z=0 which defines the exit plane, than it is to any of the current elements on the waveguide walls. If only conduction currents starting at time zero contribute to the field strength at this point, there can be no field at this observation point at a time less than the retardation time from the guide walls.

Now, as we let the guide dimensions get larger (without limit) we can show that for any specific point on the axis of the waveguide, beyond the waveguide end plane, the fields due to the currents in the walls are zero for finite time. If we take the view that the waveguide is the only structure generating em fields, and that there are no pre-existing propagating waves along the axis of the guide, then this result appears contradictory and unphysical, and so the accepted theory, and probably all the antenna calculations and simulation code based on fields being set up only by the source currents, may be in error.

Another way of looking at this problem is that the wave front progresses along the waveguide at the group velocity, which is lower than the velocity of light in the medium. Regarded as a radiating structure, the mouth of the waveguide sets off a propagating wave in free space which travels at the velocity of light. There must therefore be a contribution to the radiated fields from the center of the guide mouth, where the conduction currents are zero. Yet another insight may be obtained by appealing to Huygen’s principle in wave optics, where each point on a propagating wave front is regarded as giving rise to an outgoing hemispherical wave front. Thus if we consider radiation from a burst of microwaves propagating in free space at time zero, there are no source currents in the problem at all, within the limits of the definition of the problem.

Most antenna calculations are made assuming that the time harmonic radiation has persisted/persists for all times past and future and so the problem of what happens at the start of a radiating wave front is hidden from the analysis.

Further examination of the equations shows that A and therefore E (in the far field) lies in the preferred direction of the current sources. (The preferred direction may be taken to be an average direction over all the source currents.) The magnetic field B on the other hand forms loops around the current direction, and therefore B is at right angles to E and to the preferred direction of the current sources.

Moving charge constitutes a current. In most wires, there is a near-balance between mobile negative charge (electrons) and a background sea of positive charge (ions) which is stationary. It is therefore possible to have an “electrically neutral current” wherein the moving charge forming the current does not itself provide a source of charge density rho and therefore of electrostatic scalar potential phi.

For this reason, in many antennas textbooks, near field as well as far field radiation is assumed to be entirely determined if only the current distribution in the source is known. This is sufficient for many antennas problems. However, where there are serious discrepancies between the predictions of standard theory and the measurements on a specific antenna structure, one should look to see if there are any significant time-varying charge accumulations within the antenna conductor structure, or on any local scattering objects. One should also look to see if there are any photons emitted by transitions between electron energy levels, and to see if there are any pre-existing EM waves.

Antenna calculations

We are part way to our objective. If we know the current (and possibly charge) distributions on our antenna structure we should be able to calculate the fields anywhere for all time. However, in many antenna calculation scenarios the current distribution is not a “given” property of the problem. Often the antenna is connected to a length of transmission line (a feed), which may be coaxial cable, parallel wire line, microstrip, or it may be waveguide. The feed itself will have currents on it and may contribute to the radiation. Frequently one may assume a voltage at the junction between the feed and the antenna structure proper, but calculating the current and charge distribution on the structure after that point may be very difficult.

In aperture antenna radiation pattern calculations, a frequent ploy is to create a fictitious surface across the mouth of the aperture. Arguing backwards from the result, there will be electric and magnetic field lines intersecting this surface. One then can create an arrangement of fictitious charges and currents, and also magnetic charges and currents, on this surface. These are calculated to give rise to the local field structures on the surface, and then used to calculate the radiation field patterns at other points in space. Of course, this method requires one to have a reasonably accurate knowledge of the fields on the fictitious surface in the first place, and this may be no easier than calculating the current and charge distributions on the source structure.

Of course, if the fields are known accurately across a surface one can use Fourier Transform techniques to calculate the radiation patterns in the far field. Such techniques are frequently referred to as the “geometrical theory of diffraction”. If there are physical dielectric or magnetic obstacles in the near field then calculation of the perturbations of the field patterns by the objects may be necessary, such methods may be grouped under the heading “physical theory of diffraction”.

One of the difficulties with all antenna calculations on complex structures is that in most cases the measurement techniques available do not have sufficient precision and accuracy to determine the validity of the calculation method used. Thus many antenna calculations have to be regarded as speculative; this is a problem for the simulator particularly if the method used consumes large amounts of computing resources to little avail.

Diodes & Transistors

In the early days of electricity there were only two groups of material: insulators and conductors. Insulators are matters, which do not allow the flow of electric current through them. Glass, porcelain, dry air and dry wood are well known insulators. Metals are known to be good conductors, with copper and silver among the best. The conductivity of a particular material depends on the number of free electrons present in it.

There is another group of material known as semiconductors. Semiconductors like germanium and silicon are bad conductors of electricity in their purest form. But when certain impurities (indium or arsenic, which have a slightly different atomic structure from that of germanium or silicon) are added in the form of carefully controlled quantities, either an increase of free electrons or deficiency of electrons results. A semiconductor is called an n-type semiconductor where conduction takes place by reason of excess free electrons. A semiconductor is called a p-type semiconductor where conduction takes place due to freely moving ‘holes’ (positively charged) which replace electrons displaced by random electron movement in the material.

DIODES

When pieces of p-type and n-type semiconductors are joined together, a p-n junction results. Flow of electric current through such a junction is possible only when the positive pole of the battery (voltage source) is connected to the p-type semiconductor and the negative pole to the n-type semiconductor.

This is called the “forward biased” condition. In this condition, positively charged holes are repelled by the battery voltage towards the junction between p and n type material. Simultaneously, the electrons in the n-type material are repelled by the negative battery voltage toward the p-n junction. Despite the presence of a potential barrier at the p-n junction, which prevents electrons and holes from moving across and combining, under the influence of the electric field of the battery the holes move to the right across the junction

and the electrons move to the left. As a result, electrons and holes combine and for each combination of that takes place near the junction, a covalent bond near the positive battery terminal breaks down, an electron is liberated and enters the positive terminal. This action creates a new hole which moves to the right toward the p-n junction.

At the opposite end, in the N-region near the negative terminal, more electrons arrive from the negative battery terminal and enter the n-region to replace the electrons lost by combination with holes near the junction. These electrons move toward the junction at the left, where they again combine with new holes arriving there. As a consequence, a relatively large current flows through the junction. The current through the external connecting wires and battery is due to that of the flow of electrons.

If, however, the polarity of the battery is reversed, i.e., the positive terminal is connected to n-type semiconductor and the negative terminal of the battery to the p-type semiconductor, the p-n junction will block the electron flow by building up a voltage barrier at the junction. The holes are now attracted to the negative battery terminal and move away from the junction because of the attraction of the positive terminal. Since there are effectively no hole and electron carriers in the vicinity of the junction, current flow stops almost completely.

This type of device is called a “solid state diode” or a semiconductor. By exploiting their property of one way flow of electric current, they can be utilized to convert alternating current to direct current (known as rectification). Without adequate filtering, the resultant d.c. is pulsating in nature.

TRANSISTORSThe simplest of the transistors are of two types-either p-n-p or n-p-n. Two p-n junction diodes can be sandwiched back to back to form a p-n-p or n-p-n junction transistor. But in a practical transistor, the center or n-type portion of the sandwich is extremely thin in comparison to the p-regions. In the 1st illustration, both the p-n junctions are reverse biased.

In this type of connection, holes in the each of p-region are attracted towards the negative battery terminal and the mobile electrons in the n-region are initially moved away from both junctions in the direction of the positive battery terminal. Due to the displacement of holes and electrons, there will be no current flow in the external circuit.

In the 2nd illustration, one of the p-n junctions is forward biased, while the other is reversed biased. In a transistor, the middle layer (here n-region) is called the base, the forward biased p-n junction is called the emitter junction and the reverse biased p-n junction is called collector junction. Due to the positive potential at the emitter junction, the holes in the p-region cross into the n-region (the base). But this region is very thin and there are very few electrons with which holes can combine. So, majority of the holes drift across the base into the collector junction. About 5 per cent of them are lost in the base region as they combine with electrons.

For each hole that is lost by combination with an electron in the base and collector areas, a covalent bond near the emitter electrode breaks down and a liberated electron leaves the emitter electrode and enters the positive battery terminal. The new hole that is formed then moves immediately toward the emitter junction, and the process is repeated.

Thus, a continuous supply of holes are injected into the emitter junction, which flow across the base region and collector junction, where they are gathered up by the negative collector voltage. The flow of current within the p-n-p transistor thus takes place by hole conduction from emitter to collector, while conduction in the external circuit is due to the conduction of electrons.

Because of the reverse bias no current can flow in the collector circuit, unless current is introduced into the emitter. Since a small emitter voltage of about 0.1 to 0.5 volt permits the flow of an appreciable emitter current, the input power to the emitter circuit is quite small. As we have seen, the collector current due to the diffusion of holes is almost as large as the emitter current. Moreover, the collector voltage can be as high as 45 volts, thus permitting relatively large output powers.

A large amount of power in the collector circuit may be controlled by a small amount of power in the emitter circuit. The power gain in a transistor (power out/power in) thus may be quite high, reaching values in the order of 1000.

The ratio of collector current to emitter current is known as alpha (a) and it is the measure of possible current amplification in a transistor. a cannot be higher than 1.

Transistor Symbols and Connection:

When transistors are operated as amplifier, three different basic circuit connections are possible: (a) Common-base, emitter input; (b) common-emitter, base input; and (c) common-collector, base-input.

Regardless of the circuit connection the emitter is always forward biased and collector is always reverse biased.

There are some narrow band (field communication) wich only modulate the frequency 1-5kHz.There are some different way to bring out the sound from the RF-signal. I will explain a way by using a “quad coil”.A FM demodulator produces an output voltage that is proportional to the instantaneous frequency of the input.There are three general categories of FM demodulator circuit:Phase-locked loop (PLL) demodulatorSlope detection/FM discriminatorQuadrature detector

They all produce an output voltage proportional to the instantaneous input frequency.I will not explain the two first types, but I will explain more about the last one.

Quadrature FM detectors use a high-reactance capacitor (C2) to produce two signals with a 90 degree phase difference. The phase-shifted signal is then applied to an LC-tuned resonant at the carrier frequency (L1 and C3). Frequency changes will then produce an additional leading or lagging phase shift into the mixer.

Single Sideband Suppressed Carrier (SSB-SC):
Single Sideband Suppressed Carrier (SSB-SC) modulation was the basis for all long distance telephone communications up until the last decade. It was called “L carrier.” It consisted of groups of telephone conversations modulated on upper and/or lower sidebands of contiguous suppressed carriers. The groupings and sideband orientations (USB, LSB) supported hundreds and thousands of individual telephone conversations.
Due to the nature of-SSB, in order to properly recover the fidelity of the original audio, a pilot carrier was distributed to all locations (from a single very stable frequency source), such that, the phase relationship of the demodulated (product detection) audio to the original modulated audio was maintained.

Also, SSB was used by the U.S. Air force’s Strategic Air Command (SAC) to insure reliable communications between their nuclear bombers and NORAD. In fact, before satellite communications SSB-was the only reliable form of communications with the bombers.

The main reason-SSB-is superior to-AM,-and most other forms of modulation is due to the following:

SSB-ver-AM
(1) Since the carrier is not transmitted, there is a reduction by 50%
of the transmitted power (-3dBm). –In AM @100% modulation: 1/2 of the power is comprised of the carrier; with the remaining (1/2) power in both sidebands.

(2) Because in SSB, only one sideband is transmitted, there is a further reduction
by 50% in transmitted power (-3dBm (+) -3dBm = -6dBm).

(3) Finally, because only one sideband is received, the receiver’s needed
bandwidth is reduced by one half–thus effectively reducing the
required power by the transmitter another 50% (-3dBm (+) -3dBm (+) -3dBm = -9dBm). –Remember, if a receiver’s bandwidth can be reduced by 50%: the needed transmitter power is also reduced by 50%, i.e., the receiver’s Signal to Noise Ratio (SNR) is improved as the receiver bandwidth is reduced. This of course implies that the signal containing the information is not lost–which is the case in this instance. –Huh? Its true: if I’m Lying, I’m Dying!

Example: A HAM running 2000 Watts AM, would sound no better than another
HAM running 250 Watts PEP (Peak Envelop Power) on-SSB.

What is Single Side-band?

Before you can understand what SSB is, you must understand how audio is transmitted via radio waves. The method by which audio is impressed on a radio signal is called modulation. The two types of modulation that most people are familiar with are AM (amplitude modulation) and FM (frequency modulation), for which the AM and FM broadcast bands were named.

The Carrier.

In an AM-modulated radio signal, a base signal, called the carrier, is continuously broadcast. The two modulating signals are called the sidebands. Any audio that you hear on an AM broadcast station is from the two sidebands. When the radio station is not transmitting any sound, you can still hear that a signal is present; that is the carrier.

These two modulating (audio) sidebands are located on either side of the carrier signal–one just above the other just below. As a result, the sideband located just above the carrier frequency is called the upper sideband and that which is located just below the carrier frequency is called the lower sideband.

The Sidebands.

The pieces that fit together to form an AM broadcast signal are quite important. Although AM signals were transmitted almost exclusively for decades, it was discovered that the AM signal could be dissected. The first amateur radio operators to experiment with these processes often used both sidebands without the carrier. This is known as double sideband (DSB). DSB was typically used in the earlier operations because it was much easier to strip out just the carrier than to strip out the carrier and one of the sidebands.

Several years later (and still true today), it was much more common in the amateur bands to transmit merely using one of the sidebands, which is known as single sideband (SSB). Single sideband transmissions can consist of either the lower sideband (LSB) or the upper sideband (USB).

If you listen to an SSB signal on an AM modulation receiver, the voices are altered and sound a lot like cartoon ducks. As a result, you must have a special SSB receiver to listen to these transmissions. Although this was often difficult for the amateur radio operators of the 1950s to obtain, it is no longer a problem with today’s modern SSB transceivers.

Broadcasters Need Fidelity.

You might wonder why SSB modulation is used for some applications and AM is used for broadcasting. Broadcasters must have excellent audio fidelity when transmitting music; otherwise, the typical radio listener will tune to another station. In order to achieve excellent fidelity when transmitting music, both sidebands and the carrier are necessary.

To produce this AM signal, the transmitter is, in effect, working as three transmitters: one to produce a strong carrier for each of the sidebands, an upper sideband, and a lower sideband. The result is that approximately half of the transmitter power is “wasted” on a blank carrier and the rest of the power is divided between the two sidebands. As a result, the actual audio output from a 600-watt AM transmitter (300 watts of carrier + 150 watts on each sideband) would be the same as the 150-watt SSB transmitter.

SSB’s High Efficiency.

Let’s run some numbers: Suppose you have a typical 5-kW broadcast transmitter. You will only be able to impress 2.5 kW of audio power on that signal. This means that each of the two sidebands will have only 1.25 kW of power. But in highly effective communications using single sideband, a single sideband signal removes the carrier and one sideband and concentrates all of its energy in one sideband. Thus, a 1-kW SSB signal will “talk” as far as a 4-kW conventional AM or FM transmitter. It is one reason why long distances can be covered effectively with SSB.

Single sideband’s benefit is not only evident on transmission. The reverse happens on receive. When you work out the math, the efficiency with an SSB signal is 16 times greater than with a conventional AM signal.

HF Signal Characteristics.

HF (high frequency) is synonymous with the more familiar term, shortwave. The only difference is that HF is the term typically used for two-way and point-to-point communications. Shortwave is typically used when referring to broadcast stations in the same range. In amateur radio, both terms are frequently used.

The HF band extends from 1700 to 30,000 kHz (1.7 to 30 MHz). To give some perspective to these numbers:

The AM broadcast band runs from 540 to 1630 kHz.

The Citizen’s Band (CB) runs from 26,960 to 27,230 kHz (within the HF band).

Television channel 2 is on 54,000 kHz. (in the VHF band).

Each of these sample frequencies has different characteristics, and it is vitally important to learn this information so that you can effectively use the HF spectrum. When talking about HF, most people list the frequencies in either kHz (kilohertz) or MHz (megahertz). This is a matter of convenience only. The base rate for frequency is the hertz (Hz), named after Heinrich Hertz, an important “father of radio.” One kHz equals 1000 Hz and one MHz equals 1,000 kHz (1 million Hz).

Radio Waves.

The Hz divisions of the radio spectrum relate directly to the frequency. Signals such as light, radio, and sound are all waves. These waves travel through the air in a manner that is somewhat similar to waves in a pond. Each radio wave has a peak and a valley. The length of each radio wave is (not surprisingly) known as the wavelength. Radio waves travel at the speed of light, so the longer each wave is, the fewer waves can arrive in one second. The number of waves that arrive per second determines the frequency.

Although the wavelength and the frequency are different ways of saying the same thing, wavelengths for radio are rarely given. In the 1920s through the 1940s, the wavelength was more frequently used than the frequency. This was probably the case because the wavelength seemed like a more tangible measurement at the time. The wavelength of the radio signal is also important because it determines the length of the antenna that you will need for receiving and especially for transmitting.

Because of the signal characteristics on the AM and FM broadcast bands, combined with the less effective internal antennas, radio signals are often thought of as being used for primarily local reception (100 miles or so). However, with two-way communications in the HF band, you are not listening for entertainment to the strongest station that you can find. You are attempting to communicate with a particular station under what could be life-threatening circumstances.

In the 1910s and 1920s, most radio enthusiasts thought that the wavelengths below 180 meters were useless, that the frequencies above the top of today’s AM broadcast band were unusable. Little did they know that the opposite was true for communications over medium to long distances. These pioneers were mislead because they didn’t yet understand the methods by which radio waves travel.

Quadrature Amplitude Modulation (QAM)-

Brief Discussion
I & Q modulation, A.K.A., QAM, is a method for sending two separate (and uniquely different) channels of information.
As you know, the carrier is shifted to create two carriers: sin and cos versions.

The two modulation inputs (analog or digital) are applied to two separate balanced modulators (BM) each of which are supplied with the sin or cos carriers, i.e., modulator #1 is supplied with the sin carrier and modulator #2 is supplied with the cos carrier.

The outputs of both modulators are algebraically summed; the result of which is now a single signal to be transmitted, containing the I & Q information.

This signal is for all intents and purposes a ‘Double Sideband Signal’ (DSB) with or without a carrier (reduced).

In the case of color television chroma, the subcarrier is transmitted as a very short burst (8 to 9 alternations); the reconstituted carrier is derived from this burst at the receiver.

This method of modulation has the advantage of reducing or eliminating intermodulation interference caused by a continuous carrier near the modulation sidebands.

Upon reception, the composite signal ( I & Q) is processed to extract a carrier replica which is again shifted in phase to create both sin and cos carriers.

These carriers are applied to two different demodulators; each demodulator outputs one of the two original signals applied in the modulation process (I & Q) at the transmitter.

In the more recent incarnations of the QAM or I & Q modulation techniques, an Analog to Digital Convertor (ADC) is used to first convert the analog input to a serialized digital bit stream and is applied to the QAM modulators; likewise at the receiver.

Modulation per se is used to impress a message (voice, image, data, etc.) on to a carrier wave for transmission. A bandlimited range of frequencies that comprise the message (baseband) is translated to a higher range of frequencies. The bandlimited message is preserved, i.e., every frequency in that message is scaled by a constant value.

Contrast this to the Linear Process of Algebraically Summing Two Sinusoids: it results in a Sum and Difference only of the two waves; there are No Products Generated.

Intermodulation is a Special Case where two (or more) sinusoids effect one another to produce undesired products, i.e., Unwanted Frequencies. Again, this can only occur when both waves share the same NonLinear device. a form of Intermodulation.

To Clarify: What is a Nonlinear Device? It is Any Active Device[1].
In normal designs, radio receivers, Stereos, etc., Intermodulation is not a problem. However, when these systems are subjected to Excessive Signal Level Input the active devices in the “Front End” are driven out of their Linear Operating Regions–into or near–Saturation and/or Cutoff, where they become, in effect, “Modulators.”

[1] Active Devices: Transistors, Diodes, ICs, etc.
Passive devices: Resistors, Capacitors, Inductors, etc.

Modulation

F1

F2

F1 + F2

Summation of F1 and F2 (Linear)

In a Linear System, when one sinusoid is Superimposed upon another, neither sinusoid is affected, and no frequencies are generated.

Multiplication of F2 by F1 (Nonlinear)

Intermodulation

F1

F2

F1 + F2

Summation of F1 and F2 (Linear)

F2 x F1

F2 + F1

F2 – F1

Products Resulting from F1 and F2 (Nonlinear)

.
Cross Modulation
(a form of Inter-modulation)
If you have ever been listening to a distant FM station while driving by an AM Broadcast station’s transmitting tower; you more than likely heard both stations–one on top of the other. That effect was “Cross Modulation,” a form of Inter-modulation.
Since an FM receiver can only receive–Demodulate–one station at a time (unlike AM which cannot separate interfering stations), that is, two stations on the same frequency, the receiver will only demodulate the stronger of the two.

In the scenario above, you heard both the distant FM station and the very close AM transmitter. The FM station’s signal, as it was entering the receiver’s “Front End,” was being Modulated by the very strong AM signal. In effect, the receiver’s RF Amplifier was acting as a Detector (rectifier) varying its bias point, which caused the amplifier’s gain to change rapidly (at the AM transmitter modulation rate). This varying gain is effectively Modulating (Multiplying) the distant FM station’s signal. By the time this “Mess” reaches the receiver’s Demodulator it appears to the Discriminator as an FM signal having two audio messages superimposed one on the other.

Capture Effect
In FM receivers, the Demodulator (Limiter/Discriminator combination) will only extract Zero Axis Crossings of the strongest of competing signals. E.g., if two signals have nearly equal strength, the stronger of the two will be “Captured” while rejecting the other. Depending on the receiver design, signals as close as <1-dB, the stronger will dominate.
That is why: when listening to a distant FM station and driving away from it and approaching another FM station on the same frequency, the stations will “bounce back and forth,” hearing one then the other, never both at the same time. It can happen so rapidly that sometimes it sounds as if they are both being demodulated simultaneously.

Constructive & Destructive Interference–“Multi-Path”
You can see this effect everyday while driving around town listening to your FM radio. As you pull up to a stop light you may notice that the station is noisy, but if you roll forward a few feet, the station clears up. It isn’t that the signal is weak where it was noisy, it was the effect of two or more competing signals (reflections) arriving at your antenna having common phase angles and amplitudes first canceling, then adding as you rolled forward for the clearer signal. This Constructive & Destructive Interference is sometimes referred to as Multi-Path.

The answer to that is easy, it is a programable frequency multiplier, usually using digital logic integrated circuits. The synthesizer is arranged to multiply a reference frequency by a programable amount to achieve just about any frequency you want. If, for example you had a reference frequency of, say, 1KHz and a “programable multiplier” then you could program the multiplier to give you 1KHz (X1), 3KHz (X3), 1.025MHz (X1025), 98.325MHz (X98325) or any other frequency you want. Sounds easy? Actually, it is so easy, once you understand some of the basics. So let us start off by building a simple synthesizer that cover 3KHz to 4000KHz (4MHz).

Basic PLL Operation

A Phase Locked Loop (PLL) consists of a Voltage Controlled Oscillator (VCO), the output frequency of which is monitored and controlled. An error voltage steers the VCO and brings it back onto the correct frequency. The error voltage is generated by a Phase Sensitive Detector (PSD) which compares the VCO frequency with a reference frequency. Consider the following block diagram:

Here we have a 1KHz reference oscillator feeding the PSD Input-B, and a VCO feeding the PSD Input-A. The output of the PSD can be a square-wave and the difference between the positive pulse and the negative is averaged by the low-pass filter (LPF). This filtering results in a DC voltage that is fed back to the VCO to increase or decrease the frequency, as required.

It is interesting to note that you can put a DC voltmeter on the DC control line and watch the DC vary. The voltage will vary if either the VCO center-frequency changes or the reference frequency changes. This circuit alone can be built using a single CD4046, but without the reference oscillator. The reference osc input can then be an external connection to make a selection of useful instruments, such as:

10Hz – 3.5MHz analogue frequency meter
455KHz FM discriminator add-on for your old HF receiver
Analogue tachometer (up to 3,500,000 rpm!!)
Slow-scan TV decoder for the HF bands
AFSK, RTTY, CW, ASCII, CTCSS, SELCALL decoder for your ham rig
Remote control decoder/optical signaling
(Insert a clever use of your own here)
The PSD signal input of the CD4046 is quite sensitive and only requires a couple of hundred millivolts of input signal to pin 14. It is DC self-biasing so all you need to do is stick a capacitor in series with your low-level input signal. For more detailed information about the CD4046 then take a look at the CD4046 Datasheet (pdf format).

The Phase Sensitive Detector

Almost any logic 2-input gate can be used as a PSD, but the more usual is a simple OR- gate or an EXCLUSIVE-OR-gate. With an EXCLUSIVE-OR gate the output frequency will be twice the input frequency, but the MARK:SPACE ratio will vary as the phase between the two input signals. When the loop is “IN LOCK” there will be about 90-degrees phase difference between the two input signals. This sort of PSD is good, cheap and simple. One drawback of it is that if the two inputs are of different frequencies then the output MARK:SPACE ratio will go continuously up and down. This will restrict the ability of the loop to achieve a lock. If the natural frequency of the oscillator in the circuit above were to be less than about 750Hz or greater than about 1.35KHz then it would never achieve a lock condition. This ability to capture the VCO is measured as the top and bottom VCO frequencies that can be captured, expressed as a ratio and know as the CAPTURE RATIO. A typical capture ratio for this type of detector is just 2:1 (piss-poor) and it will even allow the loop to lock on harmonics of the VCO.

A much nicer type of PSD is composed of four Master/Slave J-K Flip-Flops in an arrangement that will deliver a permanent HIGH (1) when the reference frequency is higher than the VCO frequency. It will also deliver a permanent LOW (0) when the reference frequency is lower than the VCO frequency. When the two are equal and IN PHASE then the output may even be totally switch OFF (TRI-STATE); delivering neither a 1 or a 0 (high-impedance). This is the more usual type of PSD used in communications equipment. A typical capture ratio for a loop with this type of detector is greater than 10:1 and limited only by the practical reality of the VCO itself.

The CD4046 integrated circuit has both the above types of detector built in. The flip-flops often being used as the loop PSD and the gate can be used as an OUT OF LOCK indicator signal. Naturally, you do not want a transmitter to transmit when not locked or you have the radio equivalent of a “loose cannon on deck”, so PSD II also has an output specifically for the lock detect function.

The Loop Filter

The loop filter comprises a resistor and capacitor to form a time-constant. The capacitor charges to the average DC voltage at the input and it is this voltage that controls the VCO. There may be an additional pole to the filter to help reduce the reference frequency that is sometimes referred to as “Synthesizer Whine” (even the non-English synthesizers can whine!). R1/C1 below are the basic filter time-constant and R3/C2 are the little extra filtering

Unfortunately, with just a simple RC network, the complete PLL is a high gain closed loop with two time-dependent elements – a multivibrator! The loop will therefore never lock, but will oscillate up and down the band. Some form of DAMPING has to be included. This is shown as R2 in the circuit below.

R1/C1 have a time-constant of 10mS which is enough to smooth out our 2KHz and give us a nice DC level. R2 is also added to introduce a little damping to prevent the whole loop from oscillating. R3/C2 have a much shorter time-constant and just help to clean up the loop voltage a little. The loop filter can be quite complex and is almost a complete subject in it’s own right, so I do not intend to go too deeply here. The only other point I wish to discuss about loop filters is the choice of time constant.

If you were to apply Frequency Modulation (FM) to the VCO, then the time-constant shall be 5x the period of your lowest modulating frequency. That is to say, if you were to transmit HiFi music at 100MHz, then your lowest modulating frequency will be typically 20Hz. The period time is therefore 1/20 second or 50mS. The time constant of the filter must therefore be 5 x 50mS = 250mS. If not then the modulation will be seen as an error and the loop will correct it – cancel out the big bass-drum in your rendition of “Silent Night”. A 250mS time constant is long, so long that it would take the loop many seconds (or minutes) to change to a new frequency. In this event you can add a “speedup” circuit that reduces the time constant if there is a large change of operating frequency.

Here the two transistors operate in a complimentary push-pull arrangement, but in audio circuits they would introduce +/- 0.7v of crossover distortion. In this circuit they do not do anything at all if the loop voltage changes by less than 0.7v DC. If the loop was to be disturbed and a voltage change of more than 0.7v occurs then one or the other transistor will bypass R1, thus reducing the time constant to R4/C1.

The Voltage Controlled Oscillator

This is usually a simple oscillator so arranged that the tuning capacitor can be varied by a varying DC voltage. This is usually done with a VARICAP (Variable Capacitance) diode. It is always well worth remembering that an RF VCO is, by definition, an “unstable oscillator”. Without good mechanical stability then it will be microphonic or drift. Coils should ALWAYS be wound on formers and be well gunged up with wax, to prevent vibrations.

Notice how there are two inputs to feed a DC voltage to the Varicap Diode. One input would be used for the PLL control voltage and the other for a modulation input. Since the tuning diode does not draw any current a very high value of series resistor can be used (470K) to feed the DC to the diode. The rest of the oscillator is a very simple and unremarkable VHF oscillator.

Those of you who have played around with my FM Wireless Microphone will no-doubt recognise the circuit. The 12pf tuning capacitor has been replaced with the tuning diode. All diodes have a variable capacitance when reverse biased and these can be pressed into service if Varicap diodes are unavailable (or too damn expensive, as they are here in Sweden). Here are a few examples of diodes that can be used:

As you can see here, Zener diodes have quite a high capacitance that can be used for normal experimental synthesizer work. Be warned, the capacitance also varies with light intensity! Shine a light on them and they change a little. This could be your source of unwanted “Mains Hum” if you have flourescent lamps in the workshop. The heavy rectifier diodes also have a lower Q that could even prevent the oscillator operating with low control voltages. It is well worth noting that as the loop control voltage rises so the capacitance falls, which means that the VCO frequency will rise as the control voltage rises.

For low-frequency work you may not need VARICAP diodes at all. A simple multivibrator circuit makes a good VCO if you vary the supply voltage to the two timing resistors. A frequency ratio of 2:1 is usually possible, but the voltage to frequency sense is inverted.

The CD4046 CMOS PLL integrated circuit also has a built-in VCO that is governed by one capacitor and one resistor. An extra resistor can be used as a frequency “offset”. This VCO has a range frequency range of 10:1 and will work from a few hertz to almost 4MH

Higher Frequencies

So-far we have only considered a PLL that generates the same frequency as our reference. It could have it’s uses, but let us now multiply a frequency by TEN and generate 10KHz. Consider our basic loop circuit from above, but with an added logic divider stage.

Here the output of the VCO is divided by 10 before feeding it into the PSD. This means that the loop will see an error and push the VCO frequency up until it has 1KHz at both the PSD inputs. This will only occur if the frequency before the divider is 10 times greater than the reference frequency. If you change the divide rate to 9 then the loop will only achieve a lock condition if the VCO delivers 9KHz. In other words, the divide rate multiplied by the reference frequency is equal to the VCO output frequency. If the divide rate were set to 1500 then the VCO frequency would have to be 1.5MHz. Note also that the output frequency will only vary in steps equal to the reference frequency.

The CD4059 CMOS Programable Divider IC may be set up as a Binary Coded Decimal (BCD) divider in the range of 3 to 14999. This will give you four decimal digits that you can program with DIP switches or even rotary thumb-wheel selector switches.

I do have a project on my homepages that was used to demonstrate the synthesizer principle. See my CMOS AF/RF Synthesizer (37Hz – 4MHz). Try to follow the above steps. Note that the CD4060 is a crystal reference oscillator.

Are you still with me? Easy stuff, so-far! So let’s progress a little. I am sure I can complicate it all and confuse everything for you!

Control from your PC?

Yes, this is quite easy, at a simple level. As already stated, you can control the VCO frequency by adjusting the divide rate. The reference frequency multiplied by your divide rate is the output frequency. Ok then, so what happens if you vary the reference frequency? The VCO (synthesiser output) frequency will also vary. This opens up new possibilities. So let us program the divider for 1000, but instead of a crystal based reference oscillator, let us connect the CD4046 PSD signal input to a 50-ohm speaker used as a microphone, via a blocking capacitor. Place the speaker/microphone over the speaker in your computer

Now open the program GW-BASIC, or any other PC based BASIC language program, and enter the code listed below. Even if you are blessed with “perfect pitch” you could try whistling, but I do recommend you use your computer – it doesn’t need to pause to breathe.

10 CLS: PRINT “(Gently) Hit space to end”20 SOUND 1000,100: IF INKEY$=” ” THEN GOTO 2030 END

Now you will generate 1,000,000 Hz (1MHz) from the VCO using a 1KHz reference frequency from the computer. But if you change the BASIC program 1000 frequency value to to read 1001 you can change the reference frequency to 1001 Hertz:

10 CLS: PRINT “(Gently) Hit space to end”20 SOUND 1001,100: IF INKEY$=” ” THEN GOTO 2030 END

You will now generate 1,001,000Hz or 1.001MHz. You can then generate radio frequency whilst controlling the synthesizer from your computer. The only snag with this method is that the sound will drive you batty. You may want to unplug the speaker in your PC and connect the synthesiser reference frequency direct to the computer. I chose not to butcher my computer, but increase the tone to 10KHz and drop the programable divider to just 100. This gave me the same 1MHz frequency, but I can vary it in 10Hz steps. I am knocking on in years and cannot really hear the tone, but it drives the cats stupid! That’s Ok, I don’t really want them in the shack anyway.

If you like this method then perhaps you should take a trip to my download section and use the test tone generator program GEN.EXE (zip file). Note that the frequency generated by your PC may be approximated – all due to the division of the PC’s internal clock not always falling on exactly the frequency programmed, but it will always be very close.

But I Want VHF and UHF!

Yes, so-far we have considered synthesizers that cover a few Hertz through to the practical limit of CMOS – about 4MHz. You could use an HEF40HCT46 PLL IC instead of the CD4046. The chip is supposed to operate at up to 15MHz, so if it is just HF you are interested in then it is time to do some experimenting. If you need to go even higher in frequency then we have to consider something else.

Those of you who have used Transistor-Transistor-Logic (TTL) will aready be aware that there are logic chips that can handle frequencies of up to 30MHz. Developments in TTL devices have resulted in “Fast TTL” that can operate at frequencies of up to 120MHz. The 74F163,for example, is a fast binary counter that can be used to make a simple synthesizer in the 100MHz range. As long as you are aware of these then you have some ideas for your own experiments. I however, will go even higher, up into the amateur 144MHz band. What we need next is a PRESCALER

Prescalers

A PRECALER is a logic device to pre-divide a VHF VCO so that simple CMOS chips can be used to process the synthesizer functions. Let us begin with the SP8793 prescaler chip. This is an 8-pin device, just the same as an Operational Amplifier. The SP7893 divides by 40/41 so that a 144MHz VCO would be divided down to just 3.6MHz. This is now well within our tortoise-slow CMOS handling speeds. We take our output directly from the 144MHz VCO, but the CMOS takes it’s output from the SP8793 at 3.6MHz, like this:

Here you can see a practical oscillator circuit operating at about 144MHz. A +6dBm output at that frequency is taken directly from the oscillator. The output is also fed into the SP8793 prescaler IC, divided by 40, then fed to the programable divider. The programable divider is set to 3600 to further divide the 3.6MHz down to 1KHz. The SP8793 prescaler is similar to TTL, but uses a slightly different technique and lower impedances. These devices are known as Emitter Coupled Logic (ECL). Much faster than TTL. I will shortly have a PCB available for this particular circuit. Note that the VCO also has a Frequency Modulation input. Notice how it is connected (470K at top left). There is no provision for deviation limiting in this circuit, that is external ano not considered in these frequency generation circuits.

The prescaler divide rate of 40 multiples the programable divider to give a total division of 144000, so you must remember to calculate your divide rate then divide by 40. This circuit also has the disadvantage that the minimum steps you can program the final frequency in is 40KHz steps. Not very convenient! but we shall see about that later on. For the moment, we can select a different output from the reference oscillator (CD4060) to give us a reference frequency of 250Hz. So to get a final frequency of 144MHz, we need a total divide rate of 40 X 14400 which makes the numbers much more convenient (the CD4059 maximum count is 14999). This gives us possible frequency steps of 250Hz X 40 = 10KHz – much more convenient. It is certainly good enough for the local oscillator (LO) of a simple VHF FM receiver.

Dual Modulus

I knew I could find something to further complicate everything. As we have seen, adding a divide-by-40 prescaler to our synthesizer we increased the minimum final frequency steps from 1KHz to 40KHz. We overcame this by further reducing the reference frequency, but this solution is not acceptable for transmitters that have to be working on frequency within a few milliseconds, or for frequency scanning and any other function that requires a fast VCO capture. So what can we do about it? The answer is DUAL MODULUS, which means having two different Prescaler divide rates.

In our synthesizer above, with the added SP8793, there are four pins all connected to the +ve 5V supply. Pin 2 is connected to set the prescaler to a divide rate of 40. If pin 2 is grounded the the SP8793 will divide by 41. In other words, the SP8793 is already a dual modulus counter, but we have not yet used it as such. Let us look at a few numbers, but we will still use our same synthesizer model with the 1KHz reference oscillator and SP8793 prescaler.

I want to synthesize 800KHz. The prescaler divides by 40, so 800 / 40 = 20. Set the programable divider to 20 and we have 800KHz. Divide by 40 twenty times. Ok – so far. So where’s the problem?

Now I want 805KHz. Divide by 40 twenty times = 800KHz. Divide by 40 twenty one times = 840KHz. It doesn’t work. BUT if I divide by 41 five times, then divide by 40 another 15 times I will have my 805KHz (41 + 41 + 41 + 41 + 41 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 = 805).

Now I want 806KHz. If I divide by 41 six times, then divide by 40 another 14 times I will have my 806KHz (41 + 41 + 41 + 41 + 41 + 41 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 = 806).

Clearly, we need another programable counter to control the 40/41 divide rate of the prescaler. The main counter we will call the “N-Counter” and the extra counter we will call the “A-Counter”. We can engineer it with a little CMOS circuit like this:

The output of the Prescaler is fed into both the N and the A counters. The N-counter is fed directly and set to the full count of 20 for our 800KHz. The A counter is set to 6, but it is fed with a signal via an AND gate. Since the output of the A-counter is 0, the inverter opens the gate for counting and the output of the counter also sets the SP8793 divide rate to 41. Now we can start counting down our 20 pulses from the prescaler, like this. Note that “Total Count” is the total divide between the VCO and the PSD.

The contents of the A-counter is ZERO after the 6th pulse and so the output changes state. This changes the modulus control to the prescaler from 0 to 1 as well as closing the AND gate, so preventing the A-counter from doing anymore counting, until the N-counter has finished. As you can see in the fourth column, the total count is now 806 which will set the VCO to 806KHz using a 1KHz reference oscillator.

So, to program a “dual-modulus” synthesizer:

Divide the final output frequency by the reference frequency and you have the total count (eg. 806KHz / 1KHz = 806).

Total count divided by Prescaler count is the N-counter value (eg. 806 / 40 = 20 with a remainder of 6).

The remainder is the count to program into the A-counter (eg. 6).

You may wish to experiment with synthesizers and heaps of CMOS, but today there are loads of chips already on the market, such as the MC145152-2 which has built in A and N counters as well as all the necessary support logic. If you want more information about this family of chips then you can download the mc145151.pdf family datasheet, which shows the MC14151 single modulus, MC14152 dual modulus, and other sysnthesizer chips in that family.

Serials With Your Chips?

So-far, we have only considered synthesizers that have loads of wires to which we can connect a load of switches, diode matrixes or splashes of solder, to program. These are all called Parallel Load synthesizers. They are great for the hobyist, but when it comes to interfacing with microprocessors there are just too many wires to handle. Besides that, most radio and communications equipment processors output the data in serial format anyway. This means that there are loads of synthesizer chips on the market designed for car radios and communications stuff. They usually have a minumum of a 1.1GHz prescaler built into the chip. To use these chips you only need an external crystal and a VCO, the rest is done internally. These are termed Serial Load synthesizers.

Let us take the example of the MC145158 “Serial-Input PLL Frequency Synthesizer”. Let us assume you have already connected your crystal, VCO and prescaler as per the data sheet and are now ready to program it. This chip has three registers to which you have to send data:

You send to the chip the R-Counter value in serial binary format to the DATA input pin, begining with the most-significant binary digit. When each data bit has been presented, just clock the CLK pin high, then low to advance to the next bit of data. When all 14 bits have been sent, you set the last bit to 1 and clock it again. This will set the R-Counter with the data from the shift register. To program the A and N-Counters you sent the 7-bits of the N-Counter (MSB first) then the 7-bits of the A-Counter (MSB first) then follow it with a 0. Again you pulse the CLK input to store each bit into the chip. The 15th bit (0) tells the chip it is not an R-Counter digit.

At this point the synthesizer chip is still working on the old frequency data and will continue to do so until you send a pulse to the ENABLE (ENB) input of the chip. At this point the synthesizer will change to the new frequency program. You can therefore pre-load the synthesizer with your transmit frequency whilst still receiving. On TX key you just hit the ENB with a pulse and you are on the TX frequency. Your logic should then pre-load the RX frequency again waiting for you to release the TX. All this information is contained in the MC14151 datasheet.