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  • jalves61 4:55 pm on February 4, 2020 Permalink | Reply
    Tags: Microwave/RF Engineering   

    Limitations of Impedance matching Networks and the Bode-Fano Criterion 

    When designing an impedance matching network for an RF application, it is important to know the limitations of the design. For example, the maximum reflection coefficient is ideally quite small, but the bandwidth should be large. The Bode-Fano Criterion can specify the limitations of various load configurations to specify how exactly this tradeoff can occur. In addition, complexity of the circuit must be taken into account. The equations differ depending on the configuration of the load impedance.


    The lossless matching networks are passive and lossless. These equations lead to the conclusion that increasing the bandwidth of the matching network can be achieved by increasing the maximum reflection efficient in the passband. In addition, a reflection of zero cannot possibly be achieved unless the bandwidth is zero. This means that a perfect match can only be achieved at a finite number of discrete frequencies (you can’t have a straight line of zero reflection within the passband, only at specific points in the passband). It also shows that as R and C increase, match quality decreases. Circuits with higher Quality factors (store energy longer) are harder to match than low Q circuits.

  • jalves61 7:15 pm on January 24, 2020 Permalink | Reply
    Tags: , , Microwave/RF Engineering   

    Fundamental Parameters of Antennas 

    To understand the details behind antennas, the vital interface between free space and a transmit/receive system, it is important to fully understand the basic properties of antennas in order to understand their performance.

    One of the main properties of an antenna is its radiation or antenna pattern. This is defined as a mathematical function of the radiation properties of the antenna as a function of space coordinates. It is important to note that this pattern is determined in the far field region (there are three main regions when studying antenna radiation: reactive near field, radiating near field, and far field). This can be a trace of the Electric or magnetic field (field pattern) or the spatial variation of the power density (power pattern). These are generally normalized with respect to the maximum value and typically are plotted in decibel scale to accentuate minor lobes. Minor lobes are any lobes that are not the major lobe. In split beam antennas, there can be multiple major lobes. The following image shows a directive antenna’s radiation pattern. Side lobes are generally undesirable and should be minimized if possible.


    The Half Power Beamwidth (HPBW or sometimes just beamwidth) can be determined by drawing two lines from the origin point to the -3dB (half power) point and seeing the resultant angle.

    Antennas are generally compared to “isotropic” antennas. These are hypothetical antennas that radiate power equally in all directions. This is not to be confused with omnidirectional antennas, which radiate power equally in the azimuthal direction. The E and H planes are defined as the plane containing the electric field vector and direction of maximum radiation and the plane containing the H vector respectively.

    The three main regions around an antenna are the reactive near field, radiating near field and far field. In the reactive near field, the radiation is reactive (eg. the E and H fields are out of phase by 90 degrees. Because the waves are not in phase and transverse, they do not propagate. In the radiating near field, the waves are not purely reactive and propagate, however the shape varies with distance. In the far field (where the radiation pattern originates from), the radiation pattern does not change with distance and the waves are transverse.

    One of the major characterizing aspects of antennas is the directivity. This is equivalent to the ratio of the radiation intensity in a certain direction over the hypothetical isotropic radiator intensity.


    The denominator represents the average power radiated in all directions. The function is the normalized radiation pattern as a function of both the elevation and azimuthal angles. It is also possible to calculate partial directivities in either the theta direction or the phi direction and total directivity is the sum of these two. For a highly directive antenna with a very narrow major lobe and negligible minor lobes, the solid angle can be approximated by the product of the half power beamwidths in two different planes.


    Another important property is antenna efficiency, which is the product of reflection efficiency, conduction efficiency, and dielectric efficiency. This takes into account all possible loss: either from a VSWR greater than 1 due to an impedance mismatch between the feedline and the antenna and conductive losses due to Joule heating from both the dielectric and the conductive parts. The antenna gain can be defined as the product of the antenna efficiency and directivity.

  • jalves61 6:07 pm on January 17, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    ARRL Examination Study (Part I) 

    The ARRL (American Radio Relay League) is an organization for amateur radio enthusiasts. In order to communicate using HAM radio, at least a technician license must be obtained. The following post is meant as a useful information guide for those wishing to obtain a license.

    The ARRL provides a complete manual as a study reference for HAMs. The book is divided into nine chapters: Basic info about ARRL, Radio and Signals, Circuit components, propagation and antennas, Amateur radio equipment, HAM communication, License regulation, operating regulation and safety. The questions come directly from each chapter (35 total, 26 to pass).


    For Radio and Signal fundamentals, it is important to know basic properties of waves including wavelength, speed of propagation, the relation between wavelength and frequency, identifying frequency bands, the frequency ranges of various bands used by HAMs and so forth. The fundamental equation for propagation of waves is c = fλ. Because radio waves are being transmitted by antennas through air, the speed of propagation is 300 million meters/sec. This is a constant value and therefore if frequency is increased, the wavelength decreases proportionally. This speed value is roughly equivalent to the speed of light in a vacuum. The property of radio waves used to identify different frequency bands is wavelength. HAMs tend to use the frequencies occupied by bands MF through UHF. It is important to know the frequency ranges of these bands.


    In this section, it is important to know prefixes for the SI unit system, so conversions between various values can be made. The following table should be committed to memory.


    The next section deals with modulation, which is a necessary function to transmit the correct signal to receiver. It is important not to set a transmit frequency to be at the edge of any band to allow for transmitter frequency drift, allow for calibration error, and so that modulation sidebands do not extend beyond the band edge. It is important to know about FM deviation (which is dependent on amplitude of the modulating signal) and that if the deviation is increased, the signal occupies more bandwidth. Setting a microphone gain too high could cause the FM signal to interfere with nearby stations. It is important to know the types of AM modulation (Double Sideband, Single Sideband, etc) and which modulation technique is best for various frequency bands. “Continuous wave” (Morse code-esque) modulation occupies the lowest bandwidth, followed by SSB modulation. The various advantages to certain modulation techniques should be understood. For example, SSB is preferential to FM because it occupies less bandwidth and has longer range. The bandwidth for each modulation technique is shown below.


    The final section of Chapter two deals with radio equipment basics. A repeater should be understood to be a station that retransmits a signal onto another channel. The following is an image of a transceiver, which transmits and receives RF signals using a TR switch to switch between each function. A repeater uses a duplexer in place of this switch to transmit and receive simultaneously.


  • jalves61 7:36 pm on January 10, 2020 Permalink | Reply
    Tags: Microwave/RF Engineering   

    Quarter Wave Transformer Matching – Using Theory of Multiple Reflections 

    There are two ways to derive an impedance value for a quarter wave transformer line. The transformer is an excellent tool to match a characteristic impedance to a purely resistive load where a large bandwidth is not required. It is much easier to find this relationship by examining it from an impedance viewpoint, however the theory of multiple reflections is an excellent topic because it illustrates the contribution of multiple impedance lines to the overall reflection coefficient.

    The following circuit with the matching transformer is shown below.


    The addition of the matching transformer introduces discontinuity at the first port. Ideally, the addition of the transformer will match the load resistance to Zo, minimizing all reflection, as will be shown. the bottom figure provides a “step by step” analysis of each trip of the wave as it travels. When the wave first hits the Zo and Z1 junction, it sees Z1 as a “load” and does not yet see the actual load resistance. Depending on the impedance match, some of the wave will be reflected and some will be transmitted. The transmitted part of the wave then travels to the load and a portion is again reflected with reflection coefficient 3. As that portion of the wave travels back to the Z1 and Zo junction, the process repeats. This process continues infinitely and results in the following equation.


    Using the definition of a geometric series and writing the reflection coefficient in terms of impedance, the equation reduces to


    The reflection is seen to reduce to zero when Z1 (the impedance of the quarter wave section of transmission line) is set to q.PNG

  • mbenkerumass 2:51 pm on December 16, 2019 Permalink | Reply
    Tags: , , , Microwave/RF Engineering   

    Half-Wave Dipole Antenna Transmitter 


    Full PDF of project:




  • mbenkerumass 10:00 am on November 29, 2019 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Microstrip Coupled Line Bandpass Filter 

    ECE435 RF/Microwave Engineering, Professor Dr. Li
    Michael Benker
    November 2019

    Microstrip Coupled Line Bandpass Filter





    Final Results:




  • mbenkerumass 5:30 pm on November 23, 2019 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Skin Effect 

    RF/Photonics Lab
    Jared Alves
    November 2019

    Skin Effect

                    The skin effect is an important characteristic of alternating current within conductors. With direct current, charges are distributed evenly when flowing through a conductor. However, due to the Skin Effect as the frequency of the conduction current is increased, the charges distribute in greater quantities towards the surface of the conductor. In other words, the current density (J) decreases with greater depth in the conductor.   As shown, the current density is per area.


    The skin depth of the conductor is the length from the surface of the conductor inward in which the majority of the charge is contained at frequencies higher than DC.


    As shown in the equation above, skin depth is inversely proportional to frequency so at higher frequency values, the effective resistance of the conductor increases which reduces the cross-sectional area, as shown below.


    The figure demonstrates that the conductor becomes more “hollow” at higher frequencies as the electric charges avoids traveling through the center. This is because the back EMF is strongest towards the center of the conductor. Maxwell’s equations explain that magnetic field strength is proportional to current and therefore as current intensity changes, so does magnetic field strength. The changing magnetic field creates an electric field opposing this change in intensity which causes the counter EMF effect. This creates an almost “Faraday cage” effect with the electrons at the center of conductor as the electric field cannot penetrate as deep into the conductor with increasing frequency.


    The skin depth is technically defined as the length from the surface to the inside of a conductor in which J (current density) decays to 1/e of Js (current density at the surface). The imaginary part of the above equation shows that for each skin depth of penetration, the current density phase is delayed by 1 radian.

  • mbenkerumass 10:33 pm on November 14, 2019 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    IP3 Distortion and Linearity 

    RF/Photonics Lab
    November 2019
    Michael Benker


    IP3 Distortion & Linearity


    Linearity is the measure of a system’s performance as an output signal being proportional to the input signal level as characterized by Ohm’s Law, V = I*R. Not every system can be expected to perform ideally and thus linearly. Devices such as diodes and transistors are examples of non-linear systems.


    The intercept point of the third order, IP3 is a measure of the linearity of a system. IP3 is the third order of a Taylor series expansion of the input signal’s presence in the frequency domain. Being third order, this term in a Taylor series expansion is understood as distortion since it is different from the sought output signal. In contrast to the second order harmonics, which fall outside of the frequency band of the first order signal, the third order is found in the same frequency band as the original or first order signal. Similarly, consecutive even orders (4, 6, 8, etc) are found outside of the frequency band of the first order signal. Consecutive odd orders beyond the third order such as IP5 and IP7 also cause distortion but are not of primary focus since the amplitude of these order signals are weaker after consequent exponentiation.

    The meaning of an intercept point of an nth order (IPn) on a dBm-dBm axis is the point at which the first-order and nth-order powers would be equal for a given input power. In the case of IP3, this indicates the power level needed for a third-order power to potentially drown out the first-order signal with distortion. The 1 dB compression point defines the range of linear operation for a system.



  • mbenkerumass 5:53 pm on November 13, 2019 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Scattering Parameters 

    RF/Photonics Lab
    Jared Alves
    November 2019

    Scattering Parameters

    After the mid-1900s, high frequency networks became increasingly prevalent. When analyzing low frequency circuits parameters such as voltages and currents are easily realized. From these signals, Y and Z (admittance and impedance) parameters can be used to describe a network. For the Radio Frequency and Microwave range, S parameters are much more applicable when studying a network of a single port or multiple ports. Each S parameter can be placed in an NxN square matrix where N is the number of ports. For a single port network, only the parameter S11 (also known as ᴦ (gamma or voltage reflection coefficient)) can be realized. The S parameters are unitless because they are ratios of voltages. The parameters can be viewed as both reflection and transmission coefficients for multi-port networks. S parameters with subscripts of the same number are reflection coefficients, as they describe the ratio of voltage waves at a single port (reflected to incident).

    For a two-port network, only parameters S11, S12, S21, S22 exist. For a simple network like this, S11 represents return loss or reflection at port 1. S22 is the output reflection coefficient.  S12 and S21 are transmission coefficients where the first subscript is the responding port and the second the incident port. For example, S21 would be the “forward gain” at port 2 incident from port 1. The following diagram shows an abstracted view of a two-port network, where each “a” and “b” are normalized by the system’s characteristic impedance. Each S parameter can be calculated by terminating a port with a matched load equal to the characteristic impedance. For example, when calculated return loss for a two-port network, port 2 should be terminated by a matched load reducing a2 to zero.  For calculating S1,2 or S2,2 port 1 would be terminated with a matching load to reduce a1 to zero. Each “a” is an incident wave and “b” a reflected wave. Having a matched load at a port results none of the incident wave being reflected due to impedance mismatching.610

    This leads to the following voltage ratios:


    An amplitude with a negative superscript indicates a reflected wave, and an amplitude with a positive superscript indicates a forward propagating wave.



  • mbenkerumass 5:29 pm on November 12, 2019 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Smith Chart 

    RF/Photonics Lab
    Jared Alves
    November 2019

    Smith Chart


    The Smith Chart, named after laboratories engineer Phillip Smith, is a graphical tool for solving RF transmission line problems. There are many specific uses for a Smith Chart, but it is most commonly used to visually represent impedance matching problems. Although paper Smith Charts are outdated, RF equipment such as Network Analyzers display information using the chart as well.

    The Smith Chart is a unit circle (radius of one) plotted on the complex plane of the voltage reflection coefficient (ᴦ – gamma). As with any complex plane, the vertical axis is the imaginary and the horizontal axis the real. The Smith Chart can be used as an admittance or impedance chart or both. For a load impedance to be plotted on the chart, it must be normalized (divided by) the characteristic impedance of the system (Zo) which is the center of the chart. With this information in mind, it is apparent that a matched load condition would result in traveling to the center of the chart (where ZL=Zo). Along the circumference of the chart, there are two scales: wavelength and degrees. The degrees scale can be used to find the angle of the complex reflection coefficient. Since the plot is the polar representation of the reflection coefficient, if a line is drawn from the load impedance point to the center of the chart this would be considered the magnitude of the reflection coefficient. By extending the line to the circumference of the circle, the angle (in degrees) can be found. The wavelength scale shows distance across a transmission line in meters. A clockwise rotation represents moving towards the generator whereas a counter-clockwise rotation represents moving towards the load side.

    It is important to note that a Smith Chart can only be used at one specific frequency and one moment in time. This is because waves are functions of both space and time as shown by the equations:


    VF is the forward propagating voltage wave and VR is the reverse propagating voltage wave. If a transmission line system is not impedance matched, a reflected wave will exist on the line which will cause partial or fully standing waves to occur on the line (the reflected wave will add to the incident wave). For the matched condition the reflected wave is zero. Because the Smith Chart can only be used at a specific instant in time and at one frequency the first exponential term in each equation drops out. Because the reflection coefficient is the ratio of the reflected wave to the forward propagating wave, the reflection coefficient becomes:


    Where C is the ratio of the amplitudes of both waves. For a passive load, the reflection coefficient must be equal to one or less because the reflected wave cannot be greater in amplitude than the incident wave.

    Many transmission lines can be approximated as lossless and therefore have zero attenuation. This leads to:


    The propagation constant is a complex number that describes how a wave changes as it propagates down a transmission line. The real part is attenuation constant (Nepers/meter) and the imaginary part is the phase constant or wave number (radians/meter).


    For the lossless condition the attenuation is zero, as stated previously.

    On the Smith Chart, the wavelength λ = 720. This is because the reflected wave must travel the roundtrip distance moved (it must propagate forward and then back again). Using the piece of information, a half wavelength distance is one complete revolution on the chart. This leads to the conclusion that a transmission line that is a half wavelength long does not transform impedance.


    The following image shows common points on the Smith Chart.


    The left-hand side of the chart (lying on the real axis) represents a short circuit load. This makes intuitive sense because the reflection coefficient must be real and negative for a short circuit. This is because short circuits have a voltage drop of zero across them which would require a same-amplitude wave with a 180-degree phase shift to cancel the forward propagating wave. The right-hand part of the real axis represents the open circuit load, where the reflection coefficient is purely real but has no phase shift. For an open circuit, the current wave would have to be phase shifted by 180-degrees, but since the reflection coefficient is a voltage reflection coefficient it is not necessary for it to be phase shifted. As shown in the image, the upper half plane is inductive (positive reactance) and the lower half is capacitive (negative reactance).


    Smith Chart


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