practical rf design

7/28/2019 Practical Rf Design

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Practical RF Design I James M. Bryant, G4CLF

PRACTICAL R.F. DESIGNJames M. Bryant

INTRODUCTIONPractical R.F. design, the successful construction of a circuit which has been analysed to death in its

theoretical design phase, has a reputation of being a black art, which can only be acquired by the highly

talented, and then only at the price of infinite study, and possibly the sacrifice of a virgin or two. In fact

R.F. circuitry obeys very simple laws, the ones we learned in the nursery: Ohm's Law; Kirchoff's Law,

Lenz's Law and Faraday's Laws. The problem, however, lies in Murphy's Law.

FIG. 1

Murphy's Law is the subject of many engineering jokes, but, in its simplest form "If Anything Can Go

Wrong - It Will!" it states the simple truth that physical laws do not cease to operate just because we haveoverlooked or ignored them. At high frequency there are plenty of effects which are easy to overlook, but

if we adopt a systematic approach to circuit layout it is possible to consider all probable causes of circuit

malfunction.

FIG. 2

R.F. CIRCUITRY OBEYS BASIC LAWS

Ohm's Law

Kirchoff's LawFaraday's Laws

Lenz's Law&

Murphy's Law

MURPHY'S LAW

Whatever can go wrong, will go wrong.[Failsafes don't]

[Interchangeable parts aren't][A slice of buttered toast dropped on a sandy

floor will invariably fall butter side down]

The basic principle behind Murphy's Law is thatall physical laws always apply -

when ignored or overlooked they do not stop working.


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Practical RF Design II James M. Bryant, G4CLF

In this paper we shall consider some simple issues which are likely to affect the success of R.F. layouts,

namely resistance (including skin effect and the non-ideal characteristics of resistors), capacitance

(including the behaviour of real capacitors), inductance (both self inductance and mutual inductance),

noise, and the effect of current routing.

FIG. 3

RESISTANCEI shall be relieved when room-temperature superconductors are finally invented, as too many engineers

suppose that they are already available, and that copper is one of them. They then blame analog IC

manufacturers when this view proves untenable and the Applications Department receives the brunt of the

blame. The assumption that any two points connected by copper are at the same potential is erronious:

copper has a definite resistivity and the resistance of copper tracks on PCBs is frequently large enough to

affect analog and R.F. circuitry, (although it is rarely important to digital circuits).

FIG. 4

The diagram in Fig. 4 shows the effect of copper resistance at DC and L.F. At H.F. matters are

complicated by "skin effect". Inductive effects cause H.F. currents to flow only in the surface of

conductors. The skin depth (defined as the depth at which the current density has dropped to 1/e of its

value at the surface) at a frequency f is 1f

where is the permittivity of the conductor, and is its

conductivity in ohm-metres. (=410-7 henry/metre except for magnetic materials, where =4 r10-7

henry/metre [r is the relative permittivity].) For the purposes of resistance calculation, in cases where the

ISSUES AFFECTING SUCCESSFUL R.F. LAYOUT

ResistanceCapacitance

Inductance (self- and mutual)Noise

Grounding and decoupling

CONDUCTORS - NOT SUPERCONDUCTORS

12 cm of 0.5 mm PC track

Standard track thickness is 0.04 mm

for copper is 1.724 X 10-6 cm @ 25C

PCB sheet resistance is 0.43 m/sqResistance of the track is 0.1

THIS IS ENOUGH TO MATTER!


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Practical RF Design III James M. Bryant, G4CLF

skin depth is less than one fifth the conductor thickness we can assume that all the H.F. current flows in a

layer the thickness of the skin depth, and is uniformly distributed.

FIG. 5

Skin effect has the effect of increasing the resistance of conductors at quite modest frequencies and must

be considered when deciding if the resistance of wires or PC tracks will affect a circuit's performance. It

also affects the behaviour of some resistors at H.F.

SKIN EFFECT

At high frequencies inductive effects cause currents to flowonly in the surface of conductors.

Skin depth at frequency f in a conductor of resistivity ohm-metre

and permittivity henry/metre is

f

In copper the skin depth is 6 61.f

cm and

the skin resistance is 2 6 10 7. X f

/sq

(Remember that current mayflow in both sides of a PCB

[this is discussed later] and that the skin resistance formulais only valid if the skin depth is less than the conductor thickness.)


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Practical RF Design IV James M. Bryant, G4CLF

FIG. 6

Resistors are not the simple components that one would wish. In addition to resistance they haveinductance, capacitance, thermo-electric effects and noise. Each type of resistor is different: wirewound

and spirally cut film resistors are inductive, solid carbon resistors are less inductive, but noisy (and part of

the noise may be a function of the current in the resistor), all have capacitance. At H.F. it is rarely

necessary to consider temperature coefficients and thermoelectric effects.

These parasitic effects can be dealt with in one of two ways: use only components whose H.F. behaviour

has been characterised by their manufacturer (and remember that changing manufacturers may change the

nature of the parasitics), or characterise resistors yourself at the frequency at which they will be used (do,

however, remember that many resistors in R.F. circuitry are decoupled or bypassed and their H.F.

performance is unimportant - this should be verified by simple calculation, though, and never just

assumed). H.F. parasitics must never be ignored.

FIG. 7

All resistors have thermal or Johnson noise. A resistor of R ohms has noise of 4kTR Volts wherek is Boltzmann's constant, B is the bandwidth and T is the absolute temperature. This noise is intrinsic to

A "SIMPLE" RESISTOR

At HF the temperature coefficient (TC) and thermocouples can usually be ignored.

RESISTOR THERMAL NOISE

All resistors have Johnson noise of

4kTBR Volts

Where T is the absolute temperature, R is the resistance,B is the Bandwidth, and k is Boltzmann's Constant

(1.38 x 10-23 J/K).(It is possible to reduce T, B or R, but NOTk because Boltzmann is dead.)


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Practical RF Design V James M. Bryant, G4CLF

resistors (but not to reactances) and must be considered in all low-noise designs. Most modern resistors,

with the exception of carbon rod types, have very little more noise than their basic Johnson noise, but

carbon rod resistors are convenient at H.F. because of their low inductance. When they are used their noise

specification may need to be considered, although many applications of such resistors are in loads, where

noise is not important.

CAPACITORS

Capacitors are even more complex than resistors. As the diagram in Fig. 8 shows, a complete model has atleast three resistances, an inductor and three capacitances. Fortunately at H.F. the leakage and dielectric

absorption (provided they are not too great) are rarely important and the model may be simplified to two

capacitances, a resistor and an inductance. In many cases the small shunt capacitance can also be ignored.

The temperature coefficient of a capacitor is very important if it is being used in a tuned circuit.

FIG. 8

Where capacitors are used for coupling and decoupling their resistance and inductance are important, but

their variation with temperature rarely matters. Ceramic types have low resistance and inductance, but thehigh capacity ones have lousy temperature coefficients (NP0 types are fine, but tend to be larger), foil

capacitors generally have high inductance, but are stable. (There are low inductance foil types, but it may

be inadvisable to use them where there is any risk of the low inductance type being changed for a cheaper

high inductance type after the circuit has gone to production.)

EQUIVALENT CIRCUIT OF A "SIMPLE" CAPACITOR

It is even more complex than a resistor.

In most cases the simpler model is sufficiently accurate


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Practical RF Design VI James M. Bryant, G4CLF

FIG. 9

If inductance is to be minimised the lead and PC track length of capacitors must be kept as small as

possible. This does not mean just generally "short", but that the inductance in the actual circuit function

must be minimal. Fig. 9 shows both a common mistake (the leads of the capacitor C1 are short, but the

decoupling path for IC1 is very long); and the correct way to decouple an IC (the short decoupling path C2

provides for IC2 - the path would be even shorter if C2 were underneath IC2).

FIG. 10

Good R.F. design must incorporate stay capacitance. Wherever two conductors are separated by a

dielectric there is capacitance. The formulae for parallel wires, concentric spheres and cylinders, and other

more exotic structures may be found in an appropriate textbook but the commonest structure, found on all

PCBs, is the parallel plate capacitor.

CAPACITOR LEADS MUST BE SHORT

Although the leads of C1 are short the HF decoupling path of IC1 is far too long.

The decoupling path of IC2 is ideal.

CAPACITANCE

Wherever two conductors are separated by a dielectric(including air or a vacuum) there is capacitance.

For a parallel plate capacitorCE A

dr=

.0885pF

where A is the plate area in sq.cmd is the plate separation in cm& Er is the dielectric constant

Epoxy PCB material is often 1.5 mm thick and Er=4.7

Capacity is therefore approximately 2.8 pf/sq.cm


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Practical RF Design VII James M. Bryant, G4CLF

When stray capacitance appears as parasitic capacity to ground it can be minimised by careful layout and

routing, and incorporated into the design. Where stray capacity couples a signal where it is not wanted the

effect may be minimised by design but often must be cured by the use of a Faraday shield.

FIG. 11

A Faraday shield consists of a groundedconductor placed between the signal source and its destination.

It is surprising how often designers omit to ground a Faraday shield, which almost invariably makes the

problem worse than if there were no shield at all. It is good practice to ground any substantial conductor

which would otherwise float: crystal cans, coil cans, metal semiconductor packages, and structural metal.

INDUCTORS

FIG. 12

Any length of conductor has inductance and at H.F. this matters. In free space a 1 cm length of conductor

has inductance of 7-10 nH (depending on diameter), which represents an impedance of 4-6 at 100 MHz.

This may be large enough to be troublesome, but badly routed conductors are far worse as they form, in

effect, single turn coils with quite substantial inductance.

FARADAY SHIELDS

Capacitively coupled noise can be very effectively shieldedby a grounded conductive shield, known as a Faraday Shield.

But it must be grounded or it increases the problem.For this reason coil and quartz crystal cans should always be grounded.

INDUCTANCE

Any conductor has some inductanceA straight wire of length L and radius R (both mm)

has inductance 0 22

75. ln .LL

R

FHG KJNM

nH

A strip of conductor of length L, width W and thickness H (mm)

has inductance 0 22

0 2235 0 5. ln . .LL

W H

W H

L+FHG KJ++

FHG KJ+NM nH1 cm of thin wire or PC track is somewhere between 7 and 10 nH


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Practical RF Design VIII James M. Bryant, G4CLF

FIG. 13

If two such coils are close to each other we must consider theirmutualinductance too. A changing current

in one will induce an EMF in the other. Defining the problem, of course, suggests cures: reducing the area

of the coils by more careful layout, and increasing their separation. Both will reduce mutual inductance and

reducing area also reduces self inductance..

FIG. 14

It is possible to reduce inductive coupling by means of shields. At H.F. a continuous Faraday shield (mesh

will not work well here) blocks magnetic fields, provided that the skin depth at the frequency of interest is

much less than the thickness of the shield. (At LF shielding is much more complex.)

INDUCTANCE

A loop of conductor has inductance -two adjacent loops have mutual inductance.

INDUCTANCE

Inductance is reduced by reducing loop area -mutual inductance is reduced by reducing loop area

and increasing separation.Since the magnetic fields around coils are dipole fields they attenuate with the cube of the

distance - increasing separation is therefore a very effective way of reducing mutual inductance.


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Practical RF Design IX James M. Bryant, G4CLF

FIG. 15

Magnetic fields are dipole fields, and therefore the field strength diminishes with the cube of the distance.

This means that quite modest separation increases attenuation a lot. In many cases physical distance is all

that is necessary to reduce magnetic coupling to acceptable levels.

GROUNDS

FIG. 16

Kirchoff's Law suggests that return currents in ground are as important as signal currents in signal leads.

We find here another example of the "superconductor assumption" - too many engineers believe that all

points marked with a ground symbol on the circuit diagram are at the same potential. In practice ground

conductors have resistance and inductance - and potential differences.

MAGNETIC SHIELDS

At LF magnetic shielding requires Mu-Metal which isheavy, expensive and vulnerable to shock.

At HF a conductor provides effective magnetic shieldingprovided the skin depth is less than the conductor thickness.

PC foil is an effective magnetic shield above 10-20 MHz.

KIRCHOFF'S LAW

The net current at any point in a circuit is zero.OR

What flows in flows out again.OR

Current flows in circles.THEREFORE

All signals are differential.AND

Ground impedance matters.


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Practical RF Design X James M. Bryant, G4CLF

FIG. 17

The best ground arrangement on a PCB is a "ground plane" - a layer of continuous copper, generally on

one side of the board, but occasionally, in multi-layer boards, internal to it. A ground plane has minimalresistance and inductance, but its impedance may still be too great at high currents or high frequencies.

Sometimes a break in a ground plane can configure currents so that they do not interfere with each other,

sometimes physical separation of different subsystems is sufficient.

FIG. 18

It is often possible to deduce where currents flow in a ground plane, but in complex systems it may be

difficult. It is possible to measure differential voltages of as little as 5 V on a ground plane. At DC and

L.F. this is done by using an instrumentation amplifier with a gain of 1,000 to drive an oscilloscope

working at 5 mV/cm. The sensitivity at the input terminals of the inamp is 5 V/cm, there will be some

noise present on the oscilloscope trace, but it is quite possible to measure ground voltages of the order of

1 V with such simple equipment. It is important to allow a path for the bias current of the inamp, but its

common-mode rejection is so good that this bias path is not critical.

GROUND IS NOT A SUPERCONDUCTOR

These two points may not be at the same potential.

GROUND PLANE

The philosophy of ground plane is that one layer of a PCBconsists of a single plane of continuous metal.

It is assumed that all points on the plane are at the same potential.In practice it may be necessary to configure ground currents by

means of breaks in the plane, or careful placement of sub-systems.Nevertheless ground plane is generally

the most effective ground technique for RF designs.


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Practical RF Design XI James M. Bryant, G4CLF

FIG. 19

The upper frequency of most inamps is 25-50 KHz (the AD830 is an exception - it works up to 50 MHz at

low gains, but not at high gains). Above LF a better technique is to use a broadband (probably transmission

line) transformer to remove common-mode signals. Such a transformer has little or no voltage gain, so the

signal is best displayed on a spectrum analyser, with V sensitivity, rather than on an oscilloscope which

only has 5 mV or so.

If HF signal conductors run over a ground plane they form a microstrip transmission line. The

characteristic impedance of the line is defined by its dimensions and it must be correctly terminated if it is

not to behave reactively (but it is useful even if it is not correctly terminated). This feature of conductors

running over ground plane may be exploited to simplify HF layout: if the conductor strip is the correct

width there will be no impedance mismatch at a connector, alternatively microstrip of various impedancesmay be used to build impedance matching circuitry which uses nothing but PCB. Glass fibre/epoxy PCB is

somewhat lossy at VHF and UHF, but the losses may be tolerable if microstrip runs are short - if not, low

loss (and expensive) PCB material such as teflon must be used.

GROUND PLANE

To measure voltage drop in ground plane it is necessary to usea device with high common-mode rejection and low noise.

At DC and LF an instrumentation amplifier driving an oscilloscopewill give sensitivity of up to 5 V/cm - at HF and VHF abroadband transformer and a spectrum analyser can

provide even greater sensitivity.


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Practical RF Design XII James M. Bryant, G4CLF

FIG. 20

It is important to realise that current flow in a microstrip transmission line is constrained by inductive

effects. The signal current flows only on the side of the conductor next to the ground plane (its skin depth

is calculated in the normal way) and the return current flows only directly beneath the signal conductor,

not in the entire ground plane (skin effect naturally limits this current, too, to one side of the ground plane).

This is helpful in separating ground currents, but increases the resistance of the circuit.

FIG. 21

It is clear that breaks in the ground plane under a conductor carrying HF will force the return current to

flow around the break, increasing impedance. Even worse, if the break is made to allow two HF circuits to

cross, the two signals will interact. Such breaks should be avoided if at all possible. The best way to enable

two HF conductors on a ground plane to cross without interaction is to keep the ground plane continuous

MICROSTRIP TRANSMISSION LINE

When a conductor runs over a ground plane it forms a microstrip transmission line.

The characteristic impedance is377H

W Er (note that the units of H and W are unimportant).

The transmission line determines where both the signal and return currents flow.

MICROSTRIP TRANSMISSION LINE

The ground under a microstrip line must not be brokenor the HF ground current will be forced to flow around the

edge of the break, increasing impedance.

The best way of making a crossover of a microstrip lineis to pass one of the signals to a wire link which crosses

the ground plane on the opposite side from the microstrip.The return currents are thus completely isolated.


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Practical RF Design XIII James M. Bryant, G4CLF

and take one conductorto the other side of the ground plane to carry one of the signals past the other. If

the skin depth is much less than the ground plane thickness the interaction of ground currents will then be

negligible.

DECOUPLING

FIG. 22

The final issue we must consider is decoupling. The power supplies of HF circuits must be short-circuited

together and to ground at all frequencies above DC. (DC short-circuits are undesirable for reasons which I

shall not bother to discuss.) At low frequencies the impedance of supply lines is (or should be) low and sodecoupling can be accomplished by relatively few electrolytic capacitors which will not generally need to

be very close to the parts of the circuit they are decoupling, and so may be shared among several. (The

exception to this is where a component draws a large LF current, when a local, dedicated, electrolytic

should be used.)

At HF we cannot ignore the impedance of supply leads (as we have already seen in Fig. 9) and ICs must be

individually decoupled with low inductance capacitors having short leads and PC tracks. Even 2-3 mm of

extra lead/track length may make the difference between the success and failure of a circuit layout.

FIG. 23

Where the HF currents of a circuit are mostly internal (as is the case with many ADCs) it is sufficient that

we short-circuit its supplies at HF so that it sees its supplies as stiff voltage sources at all frequencies.

When it is driving a load with HF the decoupling must be arranged to ensure that the total loop in which

the load current flows is as small as possible. Fig. 23 shows an emitter follower without supply

DECOUPLING

Supplies must be short-circuited to each otherand to ground at all frequencies.

(But not at DC.)

DECOUPLING


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Practical RF Design XIV James M. Bryant, G4CLF

decoupling - the HF current in the load must flow through the power supply to return to the output stage

(remember that Kirchoff's Law says, in effect, that currents mustflow in circles). Fig. 24 shows the same

circuit with proper supply decoupling.

FIG. 24

This principle is easy enough to apply if the load is adjacent to the circuit driving it. Where the load must

be remote it is much more difficult, but there are solutions: they include transformer isolation and the use

of a transmission line. If the signal contains no DC or LF components it may be isolated with a transformer

close to the driver. Such an arrangement is shown in Fig. 25. (The nature of the connection from the

transformer to the load may present its own problems - but not of supply decoupling.)

FIG. 25

A correctly terminated transmission line constrains HF signal currents so that, to the supply decoupling

capacitors, the load appears to be adjacent to the driver. Even if the line is not precisely terminated, it will

constrain the majority of the return current and is frequently sufficient to prevent ground current problems.

DECOUPLING

DECOUPLING WITH REMOTE LOAD


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Practical RF Design XV James M. Bryant, G4CLF

FIG. 26

CONCLUSION

It is not possible in a short paper to discuss all the intricacies of successful RF construction, but we have

seen that the basic principle is to remember all the laws of nature which apply and consider their effects onthe design.

FIG. 27

In addition to the considerations of resistance, skin effect, capacitance, inductance and ground current, it is

important to configure systems so that sensitive circuitry is separated from noise sources and so that the

noise coupling mechanisms we have described (common resistance/inductance, stray capacitance, andmutual inductance) have minimal opportunity to degrade system performance. ("Noise" in this contect

means a signal we want [or which somebody wants] in a place where we don't want it, not natural noise

like thermal, shot or popcorn noise.) The general rule is to have a signal path which is roughly linear, so

that outputs are physically separated from inputs and logic and high level external signals only appear

where they are needed.

Thoughtful layout is important, but in many cases screening may be necessary as well.

DECOUPLING WITH REMOTE LOAD

SUCCESSFUL R.F. DESIGNS

Pay attention to:Resistance

CapacitanceInductanceDecoupling

Ground&

Separating sensitive circuits from noisy ones


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P ti l RF D i XVI J M B t G4CLF

FIG. 28

A final consideration is the power supply. Switching power supplies are ubiquitous today, because of their

low cost, high efficiency and reliability, and small size. But they can be a major source of HF noise, bothbroadband and at frequencies harmonically related to their switching frequency. This noise can couple into

sensitive circuitry by all the means we have discussed, and extreme care is necessary to prevent switching

supplies from ruining system performance. In addition to screening and decoupling, it is wise wherever

possible to site switching power supplies as far as possible from sensitive parts of the system. At some time

during development it is also interesting (and frightening, and helpful) to replace the switching supply with

a battery and observe the difference in noise.

FIG. 29

13 April 1994

James M. Bryant

Head of European Applications

aa

SWITCHING POWER SUPPLIES

Generate noise at every frequency under theSun (and some interstellar ones as well).

Every mode of noise transmission is present.

If you must use them you should filter, screen,keep them far away from sensitive circuits,

and still worry!

OBEY THE LAW

Unexpected behaviour of RF circuitry is almost always due to the designeroverlooking one of the basic laws of electronics.

Remember and obey Ohm, Faraday, Lenz, Maxwell, Kirchoffand MURPHY.

"Murphy always was an optimist" - Mrs. Murphy.

practical rf design

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