Tag Archives: Microwave/RF Engineering

IMD3: Third Order Intermodulation Distortion

We’ll begin a discussion on the topic of analog system quality. How do we measure how well an analog system works? One over-simplistic answer is to say that power gain determines how well a system operates. This is not sufficient. Instead, we must analyze the system to determine how well it works as intended, which may include the gain of the fundamental signal. Whether it is an audio amplifier, acoustic transducers, a wireless communication system or optical link, the desired signal (either transmitted or received) needs to be distinguishable from the system noise. Noise, although situationally problematic can usually be averaged out. The presence of other signals are not however. This begs the question, which other signals could we be speaking of, if there is supposed to be only one signal? The answer is that the fundamental signal also comes with second order, third order, fourth order and higher order distortion harmonic and intermodulation signals, which may not be averaged from noise. Consider the following plot:

We usually talk about Third Order Intermodulation Distortion or IMD3 in such systems primarily. Unlike the second and fourth order, the Third Order Intermodulation products are found in the same spectral region as the first order fundamental signals. Second and fourth order distortion can be filtered out using a bandpass filter for the in-band region. Note that the fifth order intermodulation distortion and seventh order intermodulation distortion can also cause an issue in-band, although these signals are usually much weaker.

Consider the use of a radar system. If a return signal is expected in a certain band, we need to be able to distinguish between the actual return and differentiate this from IMD3, else we may not be able to trust our result. We will discuss next how IMD3 is avoided.

MMIC – A Revolution in Microwave Engineering

One of the most revolutionary inventions in microwave engineering was the MMIC (Monolithic microwave integrated circuits) for high frequency applications. The major advantage of the MMIC was integrating previously bulky components into non-discrete tiny components of a chip. The subsequent image shows the integrated components of the MMIC – spiral inductors (red), FETs (blue) for example.

It is apparent that smaller transistors are present towards the input of the MMIC. This is because less power is required to amplify the weak input signals. As the signals become stronger, higher power (and hence a larger FET) is required. The input terminal (given by the arrow) is the gate and the output the drain. Like almost all RF devices, MMIC’s output and input are usually matched to 50 ohms, making them easy to cascade.

Originally, MMICs found their place within DoD for usage in phased array systems in fighter jets. Today, they are present in cellular phones, which operate in the GHz range much like military RADARs. MMICs have switched from MESFET configurations to HEMTs, which utilize compound semiconductors to create heterostructures. MMICs can be fabricated using Silicon (low cost) or III-V semiconductors which offer higher speed. Additionally, MOSFET transistors are becoming increasingly common due to improved performance over the years. The gate of the MOSFET has been shortened from several microns to several nanometers, allowing better performance at higher frequencies.

RF Spectrum Analyzers

A Spectrum analyzer (whether in the RF Domain or optical) is a tool that is dual of the oscilloscope. An oscilloscope displays a waveform in time domain. When this is represented as a function, a Fourier transform can be used on it to obtain its spectrum. A spectrum analyzer displays this content.

Spectrum analyzers are very similar to radio receivers. A radio receiver could be classified into many types: (Super)heterodyne, crystal video, etc. Similar to a heterodyne receiver, which features a bandpass filter, mixer and low pass filter, a spectrum analyzer must tune over a specific range. This range must be very narrow, which requires a high Quality factor bandpass filter to operate. This is where the YIG (Yttrium Iron Garnet) filter comes into play. YIG has a very high quality factor and resonates when exposed to a DC magnetic field. This is what determines the spectrum analyzers “resolution bandwidth”. Of course, a narrow RBW means a less noisy display and better resolution. The tradeoff for this is increased sweep time. The sweep time is inversely proportional to the RBW squared.

A sweep generator is used to repetitively scan over the frequency band. The oscillator sweeps and repetitively mixes/multiples with the input signal and is filtered with a low pass filter. The low pass filter determines the spectrum analyzer’s “video bandwidth”.

An important concept with regards to bandwidth is thermal noise. Thermal noise is the single greatest source of noise in systems under 100 GHz. Past 100 GHz and into optics, shot noise becomes more apparent. However, bandwidth is the greatest contributor to thermal noise, as noise power is given as kTB. Since k is a constant and T has a relatively negligible effect on thermal noise (the main thing is that T is nonzero. At absolute zero, you have no thermal noise. Anything above that, you have thermal noise. The difference between a pretty cold device and a scorching hot one is only maybe 10 dBm or so. Just ballparking), this means that bandwidth has a huge effect on noise. A higher RBW increases the spectrum’s noise floor and makes it harder for closely spaced frequency components to be seen, as more frequency components are passed through the envelope detector.

Video bandwidth, on the other hand, typically determines resolution between power levels and smooths the display. It is important to note that the VBW contribution happens after data has been collected and does not affect the measurement results, whereas the RBW dictates the minimum measurable bandwidth.

Phase noise is also present in a spectrum analyzer and can affect measurements near the center frequency and results from phase jitter. Since this is pretty much a phase modulation, sidebands are produced near the center frequency which can interfere with measurement. Jitter refers to deviation from periodicity of a signal.

Noise Figure

Electrical noise is unwanted alterations to a signal of random amplitude, frequency and phase. Since RADAR is typically done at microwaves frequencies, the noise contribution of most RADAR receivers is highest at the first stages. This is mostly thermal noise (Johnson noise). Each component of a receiver has its own Noise Figure (dB) which is typically kept low through the use of a LNA (Low Noise amplifier). It is important to know that all conductors generate thermal noise when above absolute zero (0K).

Noise Power

Noise Power is the product of Boltzman’s constant, temperature in Kelvin and receiver bandwidth (k*t0*B). This is typically also expressed in dBm. This value is -174 dBm at room temperature  for a 1 Hz bandwidth. If a different receiver bandwidth is present, you can simply add the decibel equivalent of the bandwidth to this value. For example, at a 1MHz bandwidth, the bandwidth ratio is 60 dB (10*log(10^6) = 60). This value can be added to the standard 1Hz bandwidth to arrive at -114 dBm. For a real receiver, this number is scaled by the Noise Figure.

 

The Noise Figure is defined as 10*log(Na/Ni) where Na is the noise output of an actual receiver and Ni is the noise output of an ideal receiver. Alternatively these can be converted to dB and subtracted. It can also be defined as the rate at which SNR degrades. For systems on earth, Noise Figure is quite useful as temperature tends to stay around 290K (room temperature). However, for satellite communication, the antenna temperature tends to be colder than 290K and therefore effective noise temperature would be used instead.

Noise Factor is the linear equivalent of Noise Figure. For cascaded systems, the noise factor gradually decreases and decreases as shown. This explains why in a receiver chain, the initial components have a much higher effect on the Noise Figure.

noisefactor

Noise Figure is a very important Figure of Merit for detection systems where the input signal strength is unknown. For example, it is necessary to decrease the Noise Figure in the electromagnetic components of a submarine in order to detect communication and RADAR signals.

RF Over Fiber Links

The basic principle of an RF over Fiber link is to convey a radio frequency electrical signal optically through modulation and demodulation techniques. This has many advantages including reduced attenuation over long distances, increased bandwidth capability, and immunity to electromagnetic interference. In fact, Rf over fiber links are essentially limitless in terms of distance of propagation, whereas coaxial cable transmission lines tend to be limited to 300 ft due to higher attenuation over distance.

The simple RFoF link comprises of an optical source, optical modulator, fiber optic cable and a receiver.

rfof

The RF signal modulates the optical signal at its frequency (f_opt) with sidebands at the sum and difference of the RF frequency and optical signal frequency. These beat against the carrier in the photodetector to reproduce and electrical RF signal. The above picture shows amplitude modulation and direct detection method. Also, impedance matching circuitry is generally included to match the ports of the modulator to the demodulator as well as amplifiers.

Before designing an RFoF link, it must be essential to bypass a transmission line in the first place. Will the system benefit from having a lower size and weight or immunity to electromagnetic interference? Is a wide bandwidth required? If not, this sort of link may not be necessary. It also must be determined the maximum SWaP of all the hardware at the two ends of the link. Another important consideration is the temperature that the link will be exposed to (or even pressure, humidity or vibration levels) that the link will be exposed to. The bandwidth of the RF and distance of propagation must be considered, finally.

The Following Figures of Merit can be used to quantify the RFoF link:

Gain

In dB, this is defined as the Signal out (in dBm) – Signal in (dBm) or 10log(g) where g is the small signal gain (gain for which the amplitude is small enough that there is no amplitude compression)

Noise Figure

For RADAR and detection systems where the input signal strength is unknown, Noise Figure is more important than SNR. NF is the rate at which SNR degrades from input to output and is given as N_out – kTB – Gain (all in dB scale).

Dynamic Range

It is known that the Noise Floor defines the lower end of dynamic range. The higher end is limited by spurious frequencies or amplitude compression. The difference between the highest acceptable and lowest acceptable input power is the dynamic range.

For example, if defined in terms of full compression, the dynamic range would be (in dB scale) : S_in.max – MDS. where MDS is the minimum detectable signal strength power.

Scattering Parameters

Scattering parameters are frequency dependent parameters that define the loss or gain at various ports. For two port systems, this forms a 2×2 matrix. In most Fiber Optic links, the backwards isolation S_12 is equal to zero due to the functionality of the detectors and modulators (they cannot perform each other’s functions). Generally the return losses at port 2 and 1 are what are specified to meet the system requirements.

 

 

Receiver Dynamic Range

Dynamic range is pretty general term for a ratio (sometimes called DNR ratio) of a highest acceptable value to lowest acceptable value that some quantity can be. It can be applied to a variety of fields, most notably electronics and RF/Microwave applications. It is typically expressed in a logarithmic scale. Dynamic range is an important figure of merit because often weak signals will need to be received as well as stronger ones all while not receiving unwanted signals.

Due to spherical spreading of waves and the two-way nature of RADAR, losses experienced by the transmitted signal are proportional to 1/(R^4). This leads to a great variance over the dynamic range of the system in terms of return. For RADAR receivers, mixers and amplifiers contribute the most to the system’s dynamic range and Noise Figure (also in dB). The lower end of the dynamic range is limited by the noise floor, which accounts for the accumulation of unwanted environmental and internal noise without the presence of a signal. The total noise floor of a receiver can be determined by adding the noise figure dB levels of each component. Applying a signal will increase the level of noise past the noise floor, and this is limited by the saturation of the amplifier or mixer. For a linear amplifier, the upper end is the 1dB compression point. This point describes the range at which the amplifier amplifies linearly with a constant increase in dB for a given dB increase at the input. Past the 1dB compression point, the amplifier deviates from this pattern.

123

The other points in the figure are the third and second order intercept points. Generally, the third intercept point is the most quoted on data sheets, as third order distortions are most common. Assuming the device is perfectly linear, this is the point where the third order distortion line intersects that line of constant slope. These intermodulation distortion generate the terms 2f_2 – f_1 and 2f_1 – f_2. So in a sense the third order intercept point is a measure of linearity. As shown in the figure, the third order distortion has a linear slope of 3:1. The point that the line intercepts the linear output is (IIP3, OIP3). This intercept point tends to be used as more of a rule of thumb, as the system is assumed to be “weakly linear” which does not necessarily hold up in practice.

Often manual gain control or automatic gain control can be employed to achieve the desired receiver dynamic range. This is necessary because there are such a wide variety of signals being received. Often the dynamic range can be around 120 dB or higher, for instance.

Another term used is spurious free dynamic range. Spurs are unwanted frequency components of the receiver which are generated by the mixer, ADC or any nonlinear component. The quantity represents the distance between the largest spur and fundamental tone.

Microstrip Antenna – Cavity Model

The following is an alternative modelling technique for the microstrip antenna, which is also somewhat similar to the analysis of acoustic cavities. Like all cavities, boundary conditions are important. For the microstrip antenna, this is used to calculated radiated fields of the antenna.

Two boundary conditions will be imposed: PEC and PMC. For the PEC the orthogonal component of the E field is zero and the transverse magnetic component is zero. For the PMC, the opposite is true.

cavity

This supports the TM (transverse magnetic) mode of propagation, which means the magnetic field is orthogonal to the propagation direction. In order to use this model, a time independent wave equation (Helmholtz equation) must be solved.

helmholtz

The solution to any wave equation will have wavelike properties, which means it will be sinusoidal. The solution looks like:

1234

Integer multiples of π  solve the boundary conditions because the vector potential must be maximum at the boundaries of x, y and z. These cannot simultaneously be zero. The resonant frequency can be solved as shown:

res

The units work out, as the square root of the product of the permeability and permittivity in the denominator correspond to the velocity of propagation (m/s), the units of the 2π term are radians and the rest of the expression is the magnitude of the k vector or wave number (rad/m). This corresponds to units of inverse seconds or Hz. Different modes can be solved by plugging in various integers and solving for the frequency in Hz. The lowest resonant mode is found to be f_010 which is intuitively true because the longest dimension is L (which is in the denominator). The f_000 mode cannot exist because that would yield a trivial solution of 0 Hz frequency. The field components for the dominant (lowest frequency) mode are given.

1x

 

 

Microstrip Patch Antennas Introduction – Transmission Line Model

Microstrip antennas (or patch antennas) are extremely important in modern electrical engineering for the simple fact that they can directly be printed to a circuit board. This makes them necessary for things like cellular antennas for GPS, communication with cell towers and bluetooth/WiFi. Patch antennas are notoriously narrowband, especially those with a rectangular shape (patch antennas can have a wide variety of shapes). Patch antennas can be configured as single antennas or in an array. The excitation is usually fed by a microstrip line which usually has a characteristic impedance of 50 ohms.

One of the most common analysis methods for analyzing microstrip antennas is the transmission line model. It is important to note that the microstrip transmission line does not support TEM mode, unlike the coaxial cable which has radial symmetry. For the microstrip line, quasi-TEM is supported. For this mode, there is a field component along the direction of propagation, although it is small. For the purposes of the model, this can be ignored and the TEM mode which has no field component in the direction of propagation can be used. This reduces the model to:

microstrip

Where the effective dielectric constant can be approximated as:

eff

The width of the strip must be greater than the height of the substrate. It is important to note that the dielectric constant is not constant for frequency. As a consequence, the above approximation is only valid for low frequencies of microwave.

Another note for the transmission line model is that the effective length differs from the physical length of the patch. The effective length is longer by 2ΔL due to fringing effects. ΔL can be expressed as a function of the effective dielectric constant.

123

 

 

 

The Superheterodyne Receiver

“Heterodyning” is a commonly used term in the design of RF wireless communication systems. It the process of using a local oscillator of a frequency close to an input signal in order to produce a lower frequency signal on the output which is the difference in the two frequencies. It is contrasted with “homodyning” which uses the same frequency for the local oscillator and the input. In a superhet receiver, the RF input and the local oscillator are easily tunable whereas the ouput IF (intermediate frequency) is fixed.

1

After the antenna, the front end of the receiver comprises of a band select filter and a LNA (low noise amplifier). This is needed because the electrical output of the antenna is often as small as a few microvolts and needs to be amplified, but not in a way that leads to a higher Noise Figure. The typical superhet NF should be around 8-10 dB. Then the signal is frequency multiplied or heterodyned with the local oscillator. In the frequency domain, this corresponds to a shift in frequency. The next filter is the channel select filter which has a higher Quality factor than the band select filter for enhanced selectivity.

For the filtering, the local oscillator can either be fixed or variable for downconversion to the baseband IF. If it is variable, a variable capacitor or a tuning diode is used. The local oscillator can be higher or lower in frequency than the desired frequency resulting from the heterodyning (high side or low side injection).

A common issue in the superhet receiver is image frequency, which needs to be suppressed by the initial filter to prevent interference. Often multiple mixer stages are used (called multiple conversion) to overcome the image issue. The image frequencies are given below.

image

Higher IF frequencies tend to be better at suppressing image as demonstrated in the term 2f_IF. The level of attenuation (in dB) of a receiver to image is given in the Image Rejection Ratio (the ratio of the output of the receiver from a signal at the received frequency, to its output for an equal strength signal at the image frequency.

RADAR Range Resolution

Before delving into the topic of pulse compression, it is necessary to briefly discuss the advantages of pulse RADAR over CW RADAR. The main difference between the two is with duty cycle (time high vs total time). For CW RADARs this is 100% and pulse RADARs are typically much lower. The efficiency of this comes with the fact that the scattered signal can be observed when the signal is low, making it much more clear. With CW RADARs (which are much less common then pulse RADARs), since the transmitter is constantly transmitting, the return signal must be read over the transmitted signal. In all cases, the return signal is weaker than the transmitter signals due to absorption by the target. This leads to difficulties with continuous wave RADAR.  Pulse RADARs can also provide high peak power without increasing average power, leading to greater efficiency.

“Pulse Compression” is a signal processing technique that tries to take the advantages of pulse RADAR and mitigate its disadvantages. The major dilemma is that accuracy of RADAR is dependent on pulse width. For instance, if you send out a short pulse you can illuminate the target with a small amount of energy. However the range resolution is increased. The digital processing of pulse compression grants the best of both worlds: having a high range resolution and also illuminate the target with greater energy. This is done using Linear Frequency Modulation or “Chirp modulation”, illustrated below.

290px-Linear-chirp.svg

As shown above, the frequency gradually increases with time (x axis).

A “matched filter” is a processing technique to optimize the SNR, which outputs a compressed pulse.

Range resolution can be calculated as follows:

Resolution = (C*T)/2

Where T is the pulse time or width.

With greater range resolution, a RADAR can detect two objects that are very close. As shown this is easier to do with a longer pulse, unless pulse compression is achieved.

It can also be demonstrated that range resolution is proportional to bandwidth:

Resolution = c/2B

So this means that RADARs with higher frequencies (which tend to have higher bandwidth), greater resolution can also be achieved.

 

 

Mathematical Formulation for Antennas: Radiation Integrals and Auxiliary Potentials

This short paper will attempt to clarify some useful mathematical tools for antenna analysis that seem overly “mathematical” but can aid in understanding antenna theory. A solid background in Maxwell’s equations and vector calculus would be helpful.

Two sources will be introduced: The Electric and Magnetic sources (E and M respectively). These will be integrated to obtain either an electric and magnetic field directly or integrated to obtain a Vector potential, which is then differentiated to obtain the E and H fields. We will use A for magnetic vector potential and F for electric vector potential.

Using Gauss’ laws (first two equations) for a source free region:

cfr

And also the identity:

1

It can be shown that:

2

In the case of the magnetic field in response to the magnetic vector potential (A). This is done by equating the divergence of B with the divergence of the curl of A, which both equal zero. The same can be done from Gauss Law of electricity (1st equation) and the divergence of the curl of F.

Using Maxwell’s equations (not necessary to know how) the following can be derived:

3

For total fields, the two auxiliary potentials can be summed. In the case of the Electric field this leads to:

4

The following integrals can be used to solve for the vector potentials, if the current densities are known:

5

For some cases, the volume integral is reduced to a surface or line integral.

An important note: most antenna calculations and also the above integrals are independent of distance, and therefore are done in the far field (region greater than 2D^2/λ, where D is the largest dimension of the antenna).

The familiar duality theorem from Fourier Transform properties can be applied in a similar way to Maxwell’s equations, as shown.

mxw

In the chart, Faraday’s Law, Ampere’s Law, Helmholtz equations and the above mentioned integrals are shown. To be perfectly honest, I think the top right equation is wrong. I believe is should have permittivity rather than permeability.

Another important antenna property is reciprocity… that is the receive and transmit radiation patterns are the same , given that the medium of propagation is linear and isotropic. This can be compared to the reciprocity theorem of circuits, meaning that a volt meter and source can be interchanged if a constant current or voltage source is used and the circuit components are linear, bilateral and discrete elements.

 

The Cavity Magnetron

The operation of a cavity magnetron is comparable to a vacuum tube: a nonlinear device that was mostly replaced by the transistor. The vacuum tube operated using thermionic emission, when a material with a high melting point is heated and expels electrons. When the work function of a material is overcome through thermal energy transfer to electrons, these particles can escape the material.

Magnetrons are comprised of two main elements: the cathode and anode. The cathode is at the center and contains the filament which is heated to create the thermionic emission effect. The outside part of the anode acts as a one-turn inductor to provide a magnetic field to bend the movement of the electrons in a circular manner. If not for the magnetic field, the electrons would simple be expelled outward. The magnetic field sweeps the electrons around, exciting the resonant cavities of the anode block.

The resonant cavities behave much like a passive LC filter circuit which resonate a certain frequency. In fact, the tipped end of each resonant cavity looks much like a capacitor storing charge between two plates, and the back wall acts an inductor. It is well known that a parallel resonant circuit has a high voltage output at one particular frequency (the resonant frequency) depending on the reactance of the capacitor and inductor. This can be contrasted with a series resonant circuit, which has a current peak at the resonant frequency where the two devices act as a low impedance short circuit. The resonant cavities in question are parallel resonant.

Just like the soundhole of a guitar, the resonant cavity of the magnetron’s resonance frequency is determined by the size of the cavity. Therefore, the magnetron should be designed to have a resonant frequency that makes sense for the application. For a microwaves oven, the frequency should be around 2.4GHz for optimum cooking. For an X-band RADAR, this should be closer to 10GHz or around this level. An interesting aspect of the magnetron is when a cavity is excited, another sequential cavity is also excited out of phase by 180 degrees.

The magnetron generally produces wavelength around several centimeters (roughly 10 cm in a microwave oven). It is known as a “crossed field” device, because the electrons are under the influence of both electric and magnetic fields, which are in orthogonal directions. An antenna is attached to the dipole for the radiation to be expelled. In a microwaves oven, the microwaves are guided using a metallic waveguide into the cooking chamber.

unnamed

 

The Half Wave Dipole Antenna

The dipole is a type of linear antenna which commonly features two monopole antennas of a quarter wavelength in size bent at 90 degree angles to each other. Another common size for the dipole is 1.25λ. These sizes will be discussed later.

It is important for beginning the study of the dipole antenna to discuss the infinitesimal dipole. This is the dipole which is smaller than 1/50 of the wavelength and is also known as a Hertzian dipole. This is an idealized component which does not exist, although it can serve as an approximation to large antennas which can be broken into smaller segments. The mathematics behind this can be found in “Antenna theory:Analysis and Design” by Constantine Balanis.

More importantly, three regions of radiation can be defined: the far field (where the radiation pattern is constant – this is where the radiation pattern is calculated), the reactive near field and the radiative near field.

regions

As shown in the image, the reactive near field is when the range is less than the wavelength divided by 2π or when the range is less than 1/6 of the wavelength. The electric and magnetic fields in this region are 90 degrees out of phase and do not radiate. It is known that the E and H fields must be in phase to propagate. The radiating near field is where the range is between 1/6 of the wavelength and the value 2D^2 divided by the wavelength. This is also known as the Fresnel zone. Although the radiation pattern is not fully formed, propagating waves exist in this region. For the far field, r must be much, much greater than λ/2π.

The radiating patterns of the dipole antenna is pictured below, with both the E and H planes. The E plane (elevation angle pattern) is pictured on the bottom right and the H plane (Azimuthal angle) beside it on the left. The plots are given in dB scale. The radiation patterns can be understood by considering a pen. While facing the pen you can see the full length of the pen, but if you look down on the pen you can only see the tip or end. This is analogous to the dipole antenna where maximum radiation is broadside to the antenna and minimum radiation on the ends, leading to the figure 8 radiation pattern. When this radiation pattern in extended to three dimensions, the top left image is derived.

patterns

 

The Radar Range Equation

To derive the RADAR range equation, it is first necessary to define the power density at a distance from an isotropic radiator. An isotropic radiator is a fictional antenna that radiates equally in all directions (azimuthal and elevation angle accounted for). The power density (in watts/sq meter) is given as:

1

However, of course RADARs are not going to be isotropic, but rather directional. The power density for this can be taken directly from the isotropic radiator with an additional scaling factor (antenna gain). This simply means that the power is concentrated into a smaller surface area of the sphere. To review, gain is directivity scaled by antenna efficiency. This means that gain accounts for attenuation and loss as it travels through the input port of the antenna to where it is radiated into the atmosphere.

2

To determine the received power to a target, this value can be scaled by another value known as RCS (RADAR Cross section) which has units of square meters. The RCS of a target is dependent on three main parameters: interception, reflection and directivity. The RCS is a function of target viewing angle and therefore is not a constant. So in short, the RCS is a unit that describes how much from the target is reflected from the target, how much is intercepted by the target as well as how much as directed back towards the receiver. An invisible stealth target would have an RCS that is zero. So in order to determined received power, the incident power density is scaled by the RCS:

3

The power density back at the receiver can then be calculated from the received power, resulting in the range being to the fourth power. This means that if the range of the radar to target is doubled, the received power is reduced by 12 dB (a factor of 16). When this number is scaled by Antenna effective area, the power received at the radar can be found. However it is customary to replace this effective area (which is less than actual area due to losses) with a receive gain term:

4

5

6

The symbol η represents antenna, and is coefficient between 0 and 1. It is important to note that the RCS value (σ) is an average RCS value, since as discussed RCS is not a constant. For a monostatic radar, the two gain terms can be replaced by a G^2 term because the receive and transmitted gain tends to be the same, especially for mechanically scanned array antennas.

7

Yagi-Uda Antenna/Parasitic Array

The Yagi-Uda antenna is a highly directional antenna which operates above 10 MHz and is commonly used in satellite communications, as well as with amateur radio operators and as rooftop television antennas. The radiation pattern for the Yagi-Uda antenna shows strong gain in one particular direction, along with undesirable side lobes and a back lobe. The Yagi is similar to the log periodic antenna with a major distinction between the two being that the Yagi is designed for only one frequency, whereas the log periodic is wideband. The Yagi is much more directional, so it provides a higher gain in that one particular direction that it is designed for.

The “Yagi” antenna has two types of elements: the driven element and the parasitic elements. The driven element is the antenna element that is directly connected to the AC source in the transmitter or receiver. A reflector element (parasitic) is placed behind the driven element in order to split the undesirable back lope into two smaller lobes. By adding directive parasitic elements in front of the driven element, the radiation pattern is stronger and more directional. All of these elements are parallel to each other and are usual half wave dipoles. These elements work by absorbing and reradiating the signal from the driven element. The reflector is slightly longer (inductive) than the driven element and the director elements are slightly shorter (capacitive).

It is well known in transmission line theory that a low impedance/short circuit load will reflect all power with an 180 degree phase shift (reflection coeffecient of -1). From this knowledge, the parasitic element can be considered a normal dipole with a short circuit at the feed point. Since the parasitic elements reradiate power 180 degrees out of phase, the superposition of this wave and the wave from the transmitter leads to a complete cancellation of voltage (a short circuit). Due to the inductive effects of the reflector element and the capacitive effects of the director antennas, different phase shifts are created due to lagging or leading current (ELI the ICE man). This cleverly causes the superposition of the waves in the forward direction to be constructive and destructive in the backwards direction, increasing directivity in the forward direction.

Advantages of the Yagi include high directivity, low cost and high front to back ratio. Disadvantages include increased sizing when attempting to increase gain as well as a gain limitation of 20dB.

yagi