Category Archives: μ-Publications (Papers)

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.

Mode Converters and Spot Size Converters

 Spot size converters are important for photonic integrated circuits where a coupling is done between two different waveguide sizes or shapes. The most obvious place to find a spot size converter is between a waveguide of a PIC and a fiber coupling lens.

 Spot size converters feature tapered layers on top of a ridge waveguide for instance, to gradually change the mode while preventing coupling loss.

The below RSoft example shows how an optical path is converted from a more narrow path (such as a waveguide) to a wider path (which could be for a fiber).

While the following simulation is designed in Silicon, similar structures are realized in other platforms such as InP or GaAs/AlGaAs.

RSoft Beamprop simulation, demonstrating conversion between two mode sizes. Optical power loss is calculated in the simulation for the structure.

rsoft13.2

 This is the 3D structure. Notice the red section present carries the more narrower optical path and this section is tapered to a wider path.

rsoft13.1

 The material layers are shown:

rsoft13.3

Structure profile:

rsoft13.5

Arrayed Waveguide Grating for Wavelength Division Multiplexing

Arrayed Waveguide Grating (or AWG) is a method for wavelength division multiplexing or demultiplexing. The approach for multiplexing is to use unequal path lengths to generate a phase delay and constructive interference for each wavelength at an output port of the AWG. Demultiplexing is done with the same process, but reversed.

Arrayed Waveguide Gratings are commonly used in photonic integrated circuits. While Ring Resonators are also used for WDM, ring resonators see other uses, such tunable or static filters. Further, a ring resonator selects a single wavelength to be removed from the input. In the case of AWGs, light is separated according to wavelength. For many applications, this is a more superior WDM, as it offers great capability for encoding and modulating a large amount of information according to a wavelength.

Both the design of the star coupler and the path length difference according to the designed wavelength division make up the significant amount of complexity of this component. RSoft by Synopsys includes an AWG Utility for designing arrayed waveguide gratings.

RSoft AWG Utility Guide

Using this utility, a star coupler is created below:

Star Coupler for AWG designed in RSoft using AWG Utility

Methods of Optical Coupling

An optical coupler is necessary for transferring optical energy into or out of a waveguide. Optical couplers are used for both free-space to waveguide optical energy transmission as well as a transmission from one waveguide to another waveguide, although the methods of coupling for these scenarios are different. Some couplers selectively couple energy to a specific waveguide mode and others are multimode. For the PIC designer, both the coupling efficiency and the mode selectivity are important to consider for optical couplers.

Where the coupling efficiency η is equal to the power transmitted into the waveguide divided by the total incident power, the coupling loss (units: dB) is equal to
L = 10*log(1/η).

Methods of optical coupling include:

  • Direct Focusing
  • End-Butt Coupling
  • Prism Coupling
  • Grating Coupling
  • Tapered Coupling (and Tapered Mode Size Converters)
  • Fiber to Waveguide Butt Coupling

Direct Focusing for Optical Coupling

Direct focusing of a beam to a waveguide using a lens in free space is termed direct focusing. The beam is angled parallel with the waveguide. This is also one type of transverse coupling. This method is generally deemed impractical outside of precision laboratory application. This is also sometimes referred to as end-fire coupling.

End-Butt Coupling

A prime example of end-butt coupling is for a case where a laser is fixated to a waveguide. The waveguide is placed in front of the laser at the light-emitting layer.

Prism Couplers

Prism coupling is used to direct a beam onto a waveguide when the beam is at an oblique incidence. A prism is used to match the phase velocities of the incident beam and the waveguide.

Prism Coupling

Grating Couplers

Similar to the prism coupler, the grating coupler also functions to produce a phase match between a waveguide mode and an oblique incident beam. Gratings perturb the waveguide modes in the region below the grating, producing a set of spatial harmonics. It is through gratings that an incident beam can be coupled into the waveguide with a selective mode.

Grating Coupler in RSoft

Tapered Couplers

Explained in one way, a tapered coupler intentionally disturbs the conditions of total internal reflection by tapering or narrowing the waveguide. Light thereby leaves the waveguide in a predictable manner, based on the tapering of the waveguide.

Tapered Mode Size Converters

Mode size converters exist to transfer light from one waveguide to another with a different cross-sectional dimension.

Butt Coupling

The procedure of placing the waveguide region of a fiber directly to a waveguide is termed butt coupling.

Programs for PIC (photonic Integrated Circuit) Design

For building PICs or Photonic Integrated Circuits, there are a number of platforms that are used in industry today. Lumerical Suite is a major player for instance with built in simulators. Cadence has a platform that can simulate both photonic and electronic circuits together, which for certain applications provides a major advantage. There are two platforms that I’ve become familiar with, which are the Synopsys PIC Design Suite (available for students with an agreement, underwritten by a professor at your university to ensure it’s use is for only educational purposes) and Klayout using Nazca Design packages.

Synopsys is another great company with advanced programs for photonic simulation and PIC design. Synopsys Photonic Design Suite can include components that are designed using Rsoft. OptoDesigner is the program in the PIC design suite where PICs are designed, yet the learning curve may not be what you were hoping. The 3,000+ page manual let’s the user dive into the scripting language PheoniX, which is necessary to learn for PIC design using Synopsys. Using a scripting language means that designing your PIC can be automated, thereby eliminating repetitive designing. There also comes other advantages to this such as being able to fine tune one’s design without needing to click and drag components. Coding for PIC design might sound tedious, but if you start to use it, I think you’ll realize that it’s really not and that it’s a very powerful way of designing PICs. If you’d like to use PheoniX scripting language using the Synopsys PIC design suite, note that the scripting language is similar to C.

Synopsys PIC Design Suite, Tutorial Program for Ring Resonator

One of the greatest aspects of OptoDesigner and the PIC Design Suite is the simulation capabilities. Much like the simulations that can be run in Rsoft, these are available in OptoDesigner.

Running FDTD in OptoDesigner

The downside of Synopsys PIC Design Suite is in the difficulty of obtaining a legal copy that can be used for any and all purposes, even commercial. I mentioned that I obtained a student version. This is great for learning the software, to a certain extent. The learning stops when I would like to build something that could be sent out to a foundry for manufacture. Let’s be honest though, there is a lot to learn before getting to that point. Still, if we would even like to use a Process Design Kit (PDK) which contains the real component models for a real foundry so that you can submit your design to be built on a wafer, you will need to convince Synopsys that the PDK is only used for educational purposes and not only for learning, but as part of an education curriculum. If your university let’s you get your hands on a PDK with Synopsys Student version, you will essentially have free range to design PICs to your hearts content. If you have a student version, you’ll still have to buy a professional version if you want to design a PIC using a foundy PDK, submit it for a wafer run and sell it. I’ll let you look up the cost for that. The best way to use Synopsys is to work for a company that has already paid for the profession version, in conclusion.

Now, if you find yourself in the situation where all the simulation benefits of using OptoDesigner are outweighed by the issue of needing to perform a wafer run, you might just want to use Klayout with Nazca Design photonic integrated circuit design packages. These are both open source. Game changer? Possibly. Suddenly, you picture yourself working as an independent contractor for PIC design someday and you’ll have Klayout to thank.

Klayout and the Nazca Design packages are based on the very popular Python programming language. Coding can be done in Spyder, Notepad or even Command Prompt (lol?). If you aren’t familiar with how Python works, PIC design might move you to learn. Python takes the place of PheoniX scripting language as is used in OptoDesigner, so you still have the automation and big brain possibilities that a scripting language gives you for designing PICs. As for simulations, you’ll have to go with your gut, but you could use discrete components to design your circuit and evaluate that.

Klayout doesn’t come with a 3,000+ page manual, but you’ll likely find that it is a simpler to use than OptoDesigner. Below is a Python script, which generates a .gds file and then the file opened in Klayout.

Python Script for PIC Design in Klayout using Nazca Design packages
.gds file opened in Klayout

Ring Resonators for Wavelength Division Multiplexing

The ring resonator is a rather simple passive photonic component, however the uses of it are quite broad.

The basic concept of the ring resonator is that for a certain resonance frequency, those frequencies entering port 1 on the diagram below will be trapped in the ring of the ring resonator and exit out of port 3. Frequencies that are not of the resonance frequency will pass through to port 2.

ringres

Ring resonators can be used for Wavelength Division Multiplexing (WDM). WDM allows for the transmission of information allocated to different wavelengths simultaneously without interference. There are other methods for WDM, such as an Asymmetric Mach Zehnder Modulator.

Here I present one scheme that will utilize four ring resonators to perform wavelength division multiplexing. The fifth output will transmit the remaining wavelengths after removing the chosen wavelengths dependent on the resonating frequency (and actually, the radius) of the ring resonators.

wdm

 

 

 

The Pockels Effect and the Kerr Effect

The Electro-optic effect essentially describes the phenomena that, with an applied voltage, the refractive index of a material can be altered. The electro-optic effect lays the ground for many optical and photonic devices. One such application would be the electro-optic modulator.

If we consider a waveguide or even a lens, such as demonstrated through problems in geometrical optics, we know that the refractive index can alter the direction of propagation of a transmitted beam. A change in refractive index also changes the speed of the wave. The change of light propagation speed in a waveguide acts as phase modulation. The applied voltage is the modulated information and light is the carrier signal.

The electro-optic effect is comprised of both a linear and non-linear component. The full form of the electro-optic effect equation is as follows:

Capture

The above formula means that, with an applied voltage E, the resultant change in refractive index is comprised of the linear Pockels Effect rE and a non-linear Kerr Effect PE^2.

The Pockels Effect is dependent on the crystal structure and symmetry of the material, along with the direction of the electric field and light wave.

 

99-mod-transfer-function-rev-600w

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.

Semiconductor Growth Technology: Molecular Beam Epitaxy and MOCVD

The development of advanced semiconductor technologies presents one important challenge: fabrication. Two methods of fabrication that are being used to in bandgap engineering are Molecular Beam Epitaxy (MBE) and Metal organic chemical vapour deposition (MOCVD).

Molecular Beam Epitaxy uses high-intensity vacuums to fabricate compound semiconductor materials and compounds. Atoms or molecules containing the desired atoms are directed to a heated substrate. Molecular Beam Epitaxy is highly sensitive. The vacuums used make use of diffusion pumps or cryo-pumps; diffusion pumps for gas source MBE and cryo-pumps for solid source MBE. Effusion cells are found in MBE and allow the flow of molecules through small holes without collusion. The RHEED source in MBE stands for Reflection Hish Energy Electron Diffraction and allows for information regarding the epitaxial growth structure such as surface smoothness and growth rate to be registered by reflecting high energy electrons. The growth chamber, heated to 200 degrees Celsius, while the substrate temperatures are kept in the range of 400-700 degrees Celsius.

MBE is not suitable for large scale production due to the slow growth rate and higher cost of production. However, it is highly accurate, making it highly desired for research and highly complex structures.

MBE

 

MOCVD is a more popular method for growing layers to a semiconductor wafer. MOCVD is primarily chemical, where elements are deposited as complex chemical compounds containing the desired chemical elements and the remains are evaporated. The MOCVD does not use a high-intensity vacuum. This process (MOCVD) can be used for a large number of optoelectronic devices with specific properties, including quantum wells. High quality semiconductor layers in the micrometer level are developed using this process. MOCVD produces a number of toxic elements including AsH3 and PH3.

MOCVD is recommended for simpler devices and for mass production.

 

matscience_1

Discrete Time Filters: FIR and IIR

There are two basic types of digital filters: FIR and IIR. FIR stands for Finite Impulse Response and IIR stands for infinite impulse response. The outputs of any discrete time filter can be described by a “difference equation”, similar to a differential equation but does not contain derivatives. The FIR is described by a moving average, or weighted sum of past inputs. IIR filter difference equations are recursive in the sense that they include both a sum of weighted values of past inputs as well as a weighted average of past outputs.

fuck

As shown, this specific IIR filter difference equation contains an output term (first time on the right hand side).

The FIR has a finite impulse response because it decays to zero in a finite length of time. In the discrete time case, this means the output response of a system to a Kronecker delta input or impulse. In the IIR case, the impulse response decays, but never reaches zero. The FIR filter has zeros with only poles at  z = 0 for H(z) (system function). The IIR filter is more flexible and can contain zeroes at any location on a pole zero plot.

The following is a block diagram of a two stage FIR filter. As shown, there is no recursion but simply a weighted sum. The triangles represent the values of the impulse response at a particular time. These sort of diagrams represent the difference equations and can be expressed as the output as a function of weighted sum of the inputs. These z inverse blocks could be thought of as memory storage blocks in a computer.

800px-FIR_Filter_(Moving_Average).svg

In contrast, the IIR filter contains recursion or feedback, as the past inputs are added back to the input. This feedback leads to a nontrivial term in the denominator of the transfer function of the filter. This transfer function can be tested for stability of the filter by observing the pole zero plot in the z-domain.

IIR

Overall, IIR filters have several advantages over FIR filters in terms of efficiency in terms of implementation which means that lower order filters can be used to achieve the same result of an FIR filter. A lower order filter is less computationally expensive and hence more preferable. A higher order filter requires more operations. However, FIR filters have a distinct advantage in terms of ease of design. This mainly comes into play when trying to design filters with linear phase (constant group delay with frequency) which is very hard to do with an IIR filter.

The Acoustic Guitar – Intro

We will consider our study of sound by briefly analyzing the acoustic guitar: an instrument that uses certain physical properties to “amplify” (not really true as no energy is technically added) sound acoustically rather than through electromagnetic induction or piezoelectric means (piezoelectric pickups are common on acoustic-electric guitars however). A guitar can be tuned many ways but standard (E standard) tuning is E-A-D-G-B-E across the six strings from top to bottom, or thickest string to thinnest. The tuning is something that can be changed on the fly, which differentiates the guitar from something like a harp which the tension of the string cannot be adjusted.

Just like the tuning pegs on a guitar can be loosened or tighten to change the tension, the fretting hand can also be used to change the length of the string. Both of these affect the frequency or perceived pitch. In fact, two other qualities of the string (density and thickness) also effect the frequency. These can be related through Mersenne’s rule:

unnamed

As shown, the length and density of the string are inversely proportional to the pitch. The tension is proportional, so tightening the string will tune the string up.  The frequency is inversely proportional to string diameter.

The basic operation of the guitar is that plucking or strumming strings will cause a disturbance in the air, displacing air particles and causing buildups of pressure “nodes” and “antinodes”. This leads to the creation of a longitudinal pressure wave which is perceived by the human ear as sound. However, a string on its own does not displace much air, so the rest of the guitar is needed. The soundboard (top) of the guitar acts as an impedance matching network between the string and air by increasing the surface area of contact with the air. Although this does not amplify the sound since no external energy is applied, it does increase the sound intensity greatly. So in a sense the soundboard (typically made of spruce or a good transmitter of sound) can be thought of as something like an electrical impedance matching transformer. The acoustic guitar also employs acoustic resonance in the soundhole. As with the soundboard, the soundhole also vibrates and tends to resonate at lower frequencies. When the air in the soundhole moves in phase with the strings, sound intensity increases by about 3 dB. So basically, the sound is being coupled from the string to the soundboard, from the soundboard to the soundhole and from both the soundhole and soundboard to the external air. The bridge is the part of the guitar that couples the string vibration to the soundboard. This creates a reasonably loud pressure wave.

In terms of wood, the typical wood used for guitar making has a high stiffness to weight ratio. Spruce has an excellent stiffness to weight ratio, as it has a high modulus of elasticity and moderately low density. Rosewood tends to be used for the back and sides of a guitar. The main thing to note hear is the guitar is made of wood.. because wood does not carry vibrations well. As a result the air echos within the guitar instead, creating a sound that is pleasant to the ear. Another factor, of course is cost.

Strings are comprised of a fundamental frequency as well as harmonics and overtones, which lead to a distinct sound. If you fret a string at the twelfth fret, this is the halfway part of the string. This would be the first overtone with double the frequency. It is important to note that the frets of a guitar taper off as you go towards the bridge. This distance can be calculated since c = fλ is a constant. Each successive note is 1.0595 higher in pitch so the first fret is placed 1.0595 from the bridge. This continues on and on with 1.0595 being raised to a higher and higher power based on what fret is being observed.

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 Helical Antenna

The helical antenna is a frequently overlooked antenna type commonly used for VHF and UHF applications and provides high directivity, wide bandwidth and interestingly, circular polarization. Circular polarization provides a huge advantage in that if two antennas are circularly polarized, the will not suffer polarization loss due to polarization mismatch. It is known that circular polarization is a special case of elliptical polarization. Circular polarization occurs when the Electric field vector (which defines the polarization of any antenna) has two components which are in quadrature with equal amplitudes. In this case, the electric field vector rotates in a circular pattern when observed at the target, whether it be RHP or LHP (right hand or left hand polarized).

Generally, the axial mode of the helix antenna is used but normal mode may also be used. Usually the helix is mounted on a ground plane which is connected to a coaxial cable using a N type or SMA connector.

The helix antenna can be broken down into triangles, shown below.

traignel

The circumference of each loop is given by πD. S represents the spacing between loops. When this is zero (and hence the angle of the triangle is zero), the helix antenna reduces to a flat loop. When the angle becomes a 90 degree angle, the helix reduces to a monopole linear wire antenna. L0 represents the length of one loop and L is the length of the entire antenna. The total height L is given as NS, where N is the number of loops. The actual length can be calculated by multiplying the number of loops with the length of one loop L0.

An important thing to note is that the helix antenna is elliptically polarized by default and must be manually designed to achieve circular polarization for a specific bandwidth. Another note is that the input impedance of the antenna depends greatly on the pitch angle (alpha).

The axial (endfire) mode, which is more common occurs when the circumference of the antenna is roughly the size of the wavelength. This mode is easier to achieve circular polarization. The normal mode features a much smaller circumference and is more omnidirectional in terms of radiation pattern.

The Axial ratio is the numerical quantity that governs the polarization. When AR = 1, the antenna is circularly polarized. When AR = ∞ or 0, the antenna is linearly polarized. Any other quantity means elliptical polarization.

itsover

The axial ratio can also be approximated by:

AR

For axial mode, the radiation pattern is much more directional, as the axis of the antenna contains the bulk of the radiation. For this mode, the following conditions must be met to achieve circular polarization.

Axial

These are less stringent than the normal mode conditions.

It is also important to consider that the input impedance of these antennas tends to be higher than the standard impedance of a coaxial line (100-200 ohms compared to 50). Flattening the feed wire of the antenna and covering the ground plane with dielectric material helps achieve a better SWR.

h

This equation can be used to calculated the height of the dielectric used for the ground plane. It is dependent on the transmission line characteristic impedance, strip width and the dielectric constant of the material used.

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.