It will also be useful reading for the
Undergraduate Microwave Option,
links into the notes, problems, and examination materials
for that option.
Minimalist reading list
Extended reading list
Frequencies from about 100MHz to 2 GHz are used for communicating with low earth orbit satellites (LEOs). Since the range from ground station to satellite is only a few hundreds of km, it is not necessary to use high gain ground based antennas. Of course, there is a direct link between the beam divergence angle of an antenna and its directivity and its gain.
A high gain antenna is therefore very directional and has to be pointed with correspondingly high precision. It is an advantage if it does not have to be moved in azimuth and elevation (see antenna notes ). This restricts the use of high gain antennas largely to geostationary satellite applications. Steerable high gain antennas (see for example Tidbinbilla deep space tracking antenna) are very specialised and costly.
Typically at 12 GHz the pointing accuracy needed for a 1 metre diameter dish is of the order of a degree or two of arc. Sophisticated tracking control apparatus would be required to keep such a dish pointing at a LEO satellite, particularly for mobile applications.
One way around the steerability problem is to use an electronically steerable "phased array" antenna. These have intrinsically rather less potential gain than a dish antenna, and require a high degree of electronic microwave complexity.
Frequencies from 1-30 GHz are usually called "microwave". From 30 GHz, to say 300 GHz the frequencies are referred to as "millimetre wave". Above 300 GHz optical techniques take over, these frequencies are known as "far infrared" or "quasi optical". Guided wave techniques are only used up to about 100GHz, higher frequencies use optical bench techniques and free space propagation to get the energy from one part of a circuit to another. This may occur in "overmoded waveguide", where the microwave energy is concentrated on the axis of the waveguide and falls off at the guide walls.
Above about 30 GHz the attenuation in the atmosphere due to cloud, rain, hydro-meteors, sand, and dust makes a ground to satellite link unreliable. Such frequencies may still be used for satellite to satellite links in space. It is arguable that for such applications optical technology is better than microwave carrier technology, particularly in view of the the extensive development in fibre optics in recent years.
6-24 GHz are useful frequencies for geostationary satcoms, since fractional bandwidths of a few percent give useful real Hz bandwidths. The fractional bandwidth is defined as the bandwidth in Hz divided by the carrier frequency in Hz.
Bandwidth is in short supply because there are only a limited number of geostationary satellite positional slots around the equator.
A common frequency band for satcoms is 10-14 GHz. Use is also made of 4-6 GHz but the capacity in this band is only half as much.
Fractional bandwidth is defined as (delta f) divided by fo where fo is the band centre and (delta f) the bandwidth in Hz which is occupied by the signal or signals.
At 10 GHz, 1% fractional bandwidth gives us 100 MHz of numerical bandwidth, which is sufficient for 10 TV channels each requiring 10MHz bandwidth. At 5 GHz, 1% fractional bandwidth only gives us 5 TV channels of 10 MHz each.
The concept of fractional bandwidth is central to satcoms. Many microwave transmission systems can only work over a limited fractional bandwidth. The widest band systems, like dual directional Lange couplers, Travelling Wave Tubes (TWTs), and circulators or isolators, have only 50% to 100% fractional bandwidth. It is possible to make distributed amplifiers with wider fractional bandwidth than this, but they tend to have rather poor group-delay characteristics across the band and have rather specialised applications.
So if we are considering say a stub tuner matching network, or a set of filters used to isolate the transmit path from the receive path and to provide power-combining functions, fractional bandwidths of between 0.1 and 5% are optimum. It so happens that this allows us useful real Hz bandwidth at the frequencies under consideration, 2-20GHz, with enough capacity for important telecoms applications.
We see therefore, that it is only a fluke of nature that allows the frequencies which propagate through the atmospheric and ionospheric window also to be sufficiently high that they can carry reasonably large amounts of information with technology which is feasible.
This is summed up by the slogan
Frequency Division Multiple Access (FDMA) allows more than one signal to be modulated onto a single "carrier". The signals are stacked up in frequency on a number of different "sub-carriers" each of which requires a local oscillator and a filter. Usually the composite signal is passed through a single feed to the satellite antenna. However it is often the case that each channel has its own high power amplifier (HPA) and the signal combining is performed with signal "multiplexers".
The antenna is often common to uplink and downlink. The received signal is separated from the transmitted signal using a "Diplexer" which has both filter and directional coupler characteristics.
To extract the signals at microwave frequencies, the filters need to have steep cut-off characteristics at the band edges, approximately constant group delay within the band, and they need to have high selectivity or high Q factor and low insertion loss in-band.
For example, at 10 GHz, a 10 MHz channel only occupies 0.1% fractional bandwidth so we need a filter width only 0.001 of its centre frequency. This may be increasingly difficult as the channels get narrower and more numerous, or as the carrier frequency gets higher and consequently the fractional bandwidth per channel gets lower.
A way out of this problem is to "frequency translate" the signal centred on frequency "fo" to lower carrier frequencies. This is done using a local oscillator at frequency "f1", together with a mixer which multiplies the local oscillator signal by the information signal. This generates sum and difference frequencies, and the information after mixing is centred on a frequency fo-fl. Lower Q factor microwave filters may then be used. However, lower frequency filters are larger, heavier, and therefore less desirable for weight-critical applications, although satisfactory in a ground station receiver.
The Q factor, or quality factor, measures the width of the cavity resonance between half power points. If the frequency difference between half power points is called df, and the centre resonance is at f, then Q = f/df. We therefore see that for a simple cavity filter, which has a single resonance, the fractional bandwidth of the filter is limited to 1/Q. See your fundamental circuit theory, or second-order-differential equation theory.
The microwave currents flow in a thin surface layer of thickness about a "skin depth" from the surface. This is because electric fields cannot penetrate perfect conductors, and only penetrate real lossy conductors a little way. See the text by Kraus on Electromagnetics for a treatment if you like.
In practice the achievable microwave cavity Q depends on frequency, since the skin depth and "ohms per square" depends on frequency. The skin depth = sqrt(2/omega mu sigma) where omega = angular frequency, mu = permeability, and sigma = bulk material conductivity. Skin depth is less at higher frequencies (omega) and so less metal is available for carrying current. Thus the resistive loss increases.
Typically, Q factors can be as high as 30,000 at 1GHz and fall to 3000 at 100 GHz.
The skirt selectivity of a microwave filter depends on the number of "poles" in the filter, or on the number of independently coupled resonant elements in the filter. It is difficult to make a microwave filter having total half-power fractional bandwidth down as low as 1/Q for the individual sections.
A definition of Q is "Energy stored in the cavity divided by energy dissipated per radian of oscillation". The energy Ed dissipated per radian is related to the dissipated power Pd by the relationship Ed times angular frequency = Pd. Clearly if there are more radians per second (the frequency is higher) there are more dissipated Joules per second (Watts).
The energy stored rises with the volume, but the power dissipated rises with the surface area of the cavity inside-walls. The energy dissipated per radian rises proportional to volume, since frequency is inversely proportional to the cavity linear dimensions.
Given constant skin depth, then all cavities would have the same intrinsic Q factor. Because the skin depth falls with frequency to the half power, the Q factors achievable falls as the square root of the frequency.
If there are multiple sources of loss in a cavity filter, such that loss element i on its own would give a Q factor Qi, it should be clear that since the losses add, the overall Q factor is given by 1/Q = sigma(i)[1/Qi] and that it is the inverse Q factors which add.
Clearly one source of loss is the energy which is coupled out of the filter to the load. There is also a loading effect due to the source impedance which can extract power as well.
If we have a very high ratio of stored energy to coupled power, the "loaded Q" may be comparable to the "Intrinsic Q". The meanings of these terms should be transparently obvious. However, if the Q is large, and especially if the loaded Q is large, for a given power throughput there may be enormous amounts of stored energy in the filter, which means the fields are large. These fields accelerate any charged particles, ions, etc which may be present, and the ionic current produced causes "multipaction" corrosion in the filter. This is such a serious problem in HPA filter chains on satellites that it seriously degrades the operating life of such filters unless care is taken to avoid it.
Multipaction occurs when breakdown happens in low pressure gas, or even vacuum, in the high electric field strengths which are found on some microwave components in the transmitter path of a microwave communications system.
A condition for multipaction is that the electrons move backwards and forwards across a gap in synchronism with an RF electric field. If the secondary emission factor of the gap surfaces is greater than unity, a rapid rise in the gap electron or ion current can occur. The two main variables which indicate the occurrence of multipaction are the transit time of electrons across the gap under the RF electric field, and the secondary emission multiplication factor.
Other sources of seed electrons for the multipaction process include stray carriers from electron beams in tubes; field emission at whiskers and points on the metal surfaces; and ionisation of residual dirt and cleaning chemicals left in the component.
Usually it is necessary for the mean free path of the charge carriers in the residual gas in the gap to be of the order of the gap dimensions, or larger than the gap dimensions. For this reason, multipaction is principally a problem of high vacuum systems, including high power circulator and filter components flown on satellites where the surrounding space is at high vacuum. At the moment of impact it is possible for various modes of impaction to occur; the RF electric field can have changed by an odd number of half cycles (1/2, 3/2, 5/2,....) since the last impact on the opposite surface, for example.
Typically for small gaps of the order of 1mm, multipaction is a problem for gap voltages of about 5000V at 10GHz. The multipaction resonant voltage depends on the mode, but for a given mode the breakdown voltage varies as the square of the product of the (frequency) and the (gap dimensions).
To suppress multipaction, either the electron dynamics can be altered (eg by adding DC magnetic fields), or the secondary emission factor can be altered by using appropriate metal film technology on the surfaces. Another method is to pressurise the component with inert gas to reduce the electron mean free paths. To reduce the secondary emission ratio, technology using titanium based films has been used in high power applications, notably at the Stanford Linear Accelerator. See R W Bierce J Jasberg and J V Lebacqz, chapter 10 of "The Stanford Two-Mile Accelerator" edited by R B Neal (Benjamin, NY 1968).
The currents carried by the ionised particles severely degrade the system performance, causing undesirable intermodulation distortion, and limiting the power handling ability.
Evidence of multipaction is provided by the surface damage on the microwave component metal parts, with pitting, discolouration, and corrosion. Multipaction occurs preferentially in regions of high electric field strength. It is exacerbated on spacecraft where the low pressure residual gas in the component supports a discharge at comparatively low electric field strengths.
Multipaction is called "multi" because one charged particle hitting the metal skin of the filter can knock out a cascade of secondary particles, also charged. These in turn increase by similar multipaction and the result is a progressive breakdown of the component. The discharge is hot and energetic, and eats into the metal surfaces making them less smooth. This in turn concentrates the electric field at the points which lowers the breakdown strength even further.
One possible solution is to put solid dielectric into the filter cavity. However, such material tends to be lossy and dispersive, and the properties of the filter containing such stuff are more difficult to calculate and reproduce from sample to sample. As the dielectric strength of pressurised gas becomes higher as the pressure is raised, it is important to keep the gas inside the component at as high a pressure as possible (this will also absorb ions knocked out from the metal walls). Inert gas is obviously better than reactive gas. Also, water and water vapour should be avoided.
Another solution is to design the filter structure to adjust the electric field magnitude by keeping the spacings large. However this has important consequences for the possible frequency and group delay characteristics of the filters which can be flown. Surfaces should be smooth and corners rounded. This is particularly important at the edges of irises.
Each filter transmits a band of frequencies. It is known that filters have both amplitude and phase responses, that is, there is a shift in both amplitude and phase between input and output signals for each component frequency in the band. Only in "linear phase" filters is the signal shape undistorted on passing through the filter. The slope of the phase delay vs frequency curve has dimensions of time, this is called the group delay and if it is constant across the band then all the signal components take the same time to traverse the system (filter, wave transmission components, downlink, etc) and reconstitute by Fourier superposition to give an accurate replica of the input signal, albeit time delayed.
The number of radians of phase shift by which each frequency component in the output lags the input, is called the "phase delay". Unlike "group delay" it does not have units of time. However the phase delay time is found by multiplying the phase delay by the period of the frequency component, and dividing by 2 pi.
There is a discussion of group delay and phase delay in the signal analysis lectures.
Overall the Q decreases as the 1/2 power of the frequency.
Microwave filters for on-board use are critical components. They have to be lightweight, but dimensionally stable. It often isn't possible to design and construct them to have the desired performance without post-production adjustments, so they often come with tuning screws. These provide extra sources of loss, and can shake loose, and leak radiation from inside to outside and vice versa. They have to be temperature stable. The metal surface needs to be high conductivity to limit the resistive loss. It can be silver plated, which is often "passivated" by a very thin coating of gold, which is chemically inert. Silver is used because it has higher conductivity than copper.
Surface finish, or polish, is important in reducing losses in microwave filters. Imagine a crinkly surface ironed out and increasing in area. If the surface is rough on a scale comparable to the skin depth the surface resistance is increased because there is more distance for the surface currents to flow per length of guide or filter structure.
Flanges on filters have to be tight fitting, and have good electrical contact even after vibration in launch and ageing processes have occurred. That is usually helped by having a great many bolts around the flange. It is also helped by the addition of half wave slots in the flange. These are short circuit one end and present a short circuit at their open end. See the notes on transmission line theory.
Often it is necessary to wrap filters on the transmit side of a transponder in aluminium foil to provide further RF isolation between the strong signals inside and the sensitive receiver circuits outside.
Modern microwave filters can have a number of compartments or cavities, connected by small holes or "irises". Typically one might need between 6 and 10 such cavities. This clearly will result in a large, bulky, heavy structure and as one filter is needed for each channel many filters have to be flown. Any possible weight reduction is advantageous.
One way of doing this is to pass the signal through the same physical cavity several times in different "modes", in a circular cavity there are two TE (transverse electric) modes which are "orthogonal", that is the electric fields are at right angles and don't cross-couple. This means that if we can convert the energy from one mode to another we can pass the signal back through the cavity on another mode and have "two cavities for the price of one".
One can be even more cunning and use the TM (transverse magnetic) modes as well, and even use a larger cavity which will support several modes of the same character at a given frequency.
Designs of multi-mode cavities are continually being improved and developed; it is an active development area in many satcoms firms and if you go to work for them you may find yourselves involved in this area.
In practice mode conversion can be made by introducing protruding screws into the cavity in appropriate symmetry positions. Location of irises also serves to discriminate between modes.
Also the size and weight of cavity filters can be further reduced by including dielectrics with high permittivity; these slow the phase velocity and mean that structures are smaller for a given frequency of operation. See DRO oscillators and the discussion on "multipaction."
As a point of information, the isolation between two type-N coaxial flexible cables, which are both double sheathed with braid, is no better than about 95 dB. This is insufficient in a satellite application to keep the transmit signal out of the receiver circuits.
There is also a magnification effect due to internal satellite chassis structural electromagnetic resonances usually called "box modes".
The oscillator is an important satcoms microwave element or component. It can be made from placing a high Q cavity on the end of a transmission line containing a negative resistance, or negative differential resistance (NDR) device. Such a device might be a Gunn diode, an IMPATT or TRAPATT diode, or possibly a transistor (HEMT, HBT).
In a super-heterodyne receiver the microwave signal and the local oscillator output, usually much larger than the signal, are fed to a nonlinear device called a mixer. This multiplies the signals and produces a frequency translation to the sum and difference frequencies. The difference frequency is called the IF or intermediate frequency. The advantage is that amplification of the signal is easier at the lower fixed IF, and filters of greater fractional bandwidths may be used for selectivity. The IF amplifier establishes the bandwidth of the system.
Ahead of the mixer-lo combination is usually placed an RF amplifier, whose purpose is to select against the image frequency and to provide amplification to overcome the inherent noise present in the mixer. It is often referred to as an LNA (low noise amplifier). Characteristics of importance for the LNA is that it should be highly linear, have good overload characteristics in the presence of spurious out-of-band signals, and have a low noise figure.
Oscillators need excellent frequency stability against variations in temperature, power-supply voltage, and oscillator loading (load pulling). They need adequate power output for the application, and low noise. There needs to be some degree of tuning capability, mechanical or electrical. They should be able to be modulated in amplitude, frequency and phase. The circuit requirements should be as simple as is practicable.
Frequency stability and low noise are obtained using a high Q resonator in the frequency-determining circuit. Loose coupling to the load allows some immunity against the frequency varying with variations of load impedance.
In a typical microwave link, up and down, there may be many oscillators doing signal up and down conversions using mixers, in addition to the signal source. Noise in these oscillators will be uncorrelated between the oscillators, and the effective noise powers will add. It is clearly of the utmost importance to start with quiet oscillators, having the lowest possible noise.
If we think of a sinusoidal oscillation as a rotating phasor whose tip traces out a circle around the origin, it is clear that noise, being random, can affect the phasor either radially or tangentially. Radial variations comprise "amplitude noise" and tangential variations comprise "Phase noise".
Since most Satcoms systems use some kind of phase or angle modulation (eg QPSK) then phase noise is clearly serious. One might think one could limit noise in an oscillator by levelling the output, or putting it through some kind of clipping circuit. This in fact converts amplitude fluctuations to timing or phase fluctuations.
In TWT HPAs the group delay is strongly amplitude dependent. There is thus a large effect of AM to PM conversion (amplitude modulation to phase modulation). This also serves to turn amplitude noise into phase noise.
Having a noisy source of negative resistance can be to some extent neutralised by using a very high Q cavity as a kind of "flywheel". In many cases the high Q element can be realised by using a dielectric resonator. Such systems have the acronym DRO, "Dielectric resonator oscillator."
The advantages of the DRO over a vacuum cavity version is largely one of size and weight, and integrability. However, since the dielectrics used commonly have temperature dependent permittivity, the oscillation frequency temperature stability is compromised.
There can be many oscillators on a complete satellite link all of which can contribute phase noise. Usually, since oscillator noise is much smaller than the oscillator amplitude, these contributions of noise are less important than the large contribution from the weak received signal which may be only a few dBs above thermal noise. However, it does contribute, is significant, and should be considered.
Let us define the acronym MLO Mixer local oscillator, which is an oscillator used with a mixer to frequency- translate a band of signals.
Then on a typical satellite link we may have the following oscillators which contribute noise....
If there is on-board processing there are two more,
namely IF to baseband MLO,
The function of the first amplifier in a receiver signal processing chain is to increase the size of the signal, together with any associated noise due to the source, so that subsequent stages which contribute noise are only adding a small amount of their own noise to the amplified noise from the signal source. Of course, we can do nothing about noise which arrives along with the signal, because the definition of noise is that it is indistinguishable from the wanted signal and has to be considered as useful information. It is a general principle that, once added, noise cannot be removed.
In practice, there will be a little added noise power from the first stage amplifier, the LNA. This is designed to have a power gain of 10dB (a factor of 10 in power) or greater, and a noise figure certainly less than 3dB (at which the added noise by the fist stage LNA is just equal to the noise contributed by the source.)
Given a power gain of 10, we see the source-derived noise is 10 times larger at the output than at the input to the LNA, so at the input to the next stage we have relaxed the necessity for low noise design.
In LNA design, the device used has a minimum noise contribution at an optimum source impedance Zs. This source impedance is not optimised for maximum power transfer, in general. We therefore sacrifice some of the other desirable properties of an amplifier in the interests of low noise.
On the S11 smith chart plot, the optimum impedance Zs is a single point. It can be shown that for larger noise contributions, at a given specified noise figure there are circles of Z on the Smith chart within which the source impedance must lie for the LNA to contribute less noise than that specified.
It is possible for some amplifiers that at optimum noise figure, the source impedance can result in instability. In this case we have to be content with a somewhat higher noise figure than optimum.
The definition of the noise figure F is (signal to noise ratio at the input)/(signal to noise ratio at the output), which a little thought shows must be a number greater than unity.
The definition of noise figure f = 10 log10 (F) dB.
The noise factor F is a number, noise figure f is expressed as dB.
At a single frequency, having a small bandwidth, the spot noise figure or factor is defined.
The spot noise factor F = (total input noise to network)/(noise input due to source alone) = 1 + (Noise due to active device)/(noise due to source). Only if there is no noise contribution from the active device is the noise factor unity.
On satellites, or in satellite ground stations, HPAs have the sole purpose of providing power for radiation by an antenna. It is possible to amplify the entire radiated signal over the full band of frequencies in a single HPA. However, often in a FDMA system, individual channels have their own dedicated HPA and the power from many HPAs is combined in a passive microwave circuit before being applied to the antenna.
This is done for the following reason. Given two or more uncorrelated RF signal channels, the phasors describing the instantaneous voltages in the various channels add vectorially. The vectors lie in random directions, changing with time, and occasionally may all add up in phase. The power in an individual signal is proportional to the square of the length of an individual constituent vector, but the total power is proportional, instantaneously, to the square of the length of the resultant vector after vector addition. There has to be this handling capacity for power in the HPA. In the case of N individual equal amplitude channels then the power handling capacity of the HPA increases as N*N. On the other hand, if we amplify each channel separately and combine power after the amplifiers, the total power handling capacity is only proportional to N. If N = 16 typically, we see we need 16 times the power handling capacity in the HPA technology if we use just a single amplifier to do the job. And we see that we need 16 times the power handling capacity in the amplifier than the average radiated power we are generating. This is clearly inefficient.
The problem with power combining post-amplification is that power combiners can have overload levels of their own, and also they introduce some loss and additional complexity. Clearly this technology is inappropriate for TDMA systems.
Various device technologies are or have been used for constructing HPA stages. Vacuum tube devices include Travelling Wave Tubes (TWTs) and Klystrons. Solid state amplifiers are used at lower powers and frequencies. Often many individual transistor chips go to make up an HPA unit, and there is inbuilt power division and combining for the paths of the signals through the individual transistors. This allows for "graceful degradation", where the performance is not seriously affected if a single chip fails. Power combining and dividing for this technology tends to be done by directional couplers; often Lange Couplers are used.
TWTs have wide bandwidth, but they are nonlinear at high efficiency levels, and give rise to amplitude-to-angle modulation effects (AM-PM, AM-FM conversion) which are very undesirable in a multi-carrier satellite application. They are also noisier and less reliable than their solid-state counterparts. However, they do give higher gain and higher power output at the higher frequencies, and are comparable in weight to the SSPA technology when the associated power supplies are included.
Copyright © D.Jefferies 1995, 1996, 1997
Temporary section until the links expire
Notes and links on microwave weaponry from TBTF.com March 2001.
After the wraps came off, Lawrence Lee of Tomalak's Realm forwarded this CNET description  of a microwave weapon that causes an intense burning sensation but does no permanent damage (or so the military spokesman claims). Here's another press account , forwarded by Greenup.
Copyright © D.Jefferies 1996, 1997, 1999, 2000, 2001, 2002, 2004.