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  • mbenkerumass 10:11 am on November 9, 2019 Permalink | Reply  

    Welcome to the Students' Page for the RF/Photonics Lab at UMASS Dartmouth 


    This page is run by students at the University of Massachusetts Dartmouth RF/Photonics Lab.


    What we do in this lab:

    • RF – Radio Frequency, Microwave Electronics
    • Photonics – Lightwave Frequency Electronics, Fiber Optics, Lasers, Optics
    • Research
    • Hands-on learning


    If you are a student and you want to do research in the RF/Photonics lab, focus on the following and talk to Dr. Li:

    Mathematics, Fourier Transform, Differential Equations, Electrical Theory, Electromagnetic Theory, Communication Theory, Analog Electronics, Signal Processing (ECE 321, ECE 384), English Writing (research writing) and 3.0+ GPA

    If you would like to get in contact with the RF/Photonics Lab at UMASS Dartmouth, feel free to fill out the form on the Contact page. Also, visit the official page for the RF/Photonics Lab.
  • mbenkerumass 8:04 pm on December 2, 2019 Permalink | Reply
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    OrCAD PCB Layout 

    ECE457 Senior Design
    Michael Benker
    December 2019



    • Tuong 9:39 pm on December 2, 2019 Permalink | Reply

      Hi, What is function of this circuit?


      • mbenkerumass 7:21 am on December 3, 2019 Permalink | Reply

        Thanks for the comment! This device is proposed to adjust the volume output between an audio source and headphones relative to the sound level in the surrounding environment. Possible applications could be in noise cancelling technology, for instance.


    • Tuong 10:46 am on December 3, 2019 Permalink | Reply

      Hi Michael. Thanks for reply. Interesting! May be you can show the real board when available, plz. I just curious.


  • mbenkerumass 8:11 pm on November 30, 2019 Permalink | Reply
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    OrCAD Schematic – (Senior Design Project) 

    ECE457 Senior Design
    Michael Benker
    November 2019

    OrCAD Schematic

    The schematic below was made using OrCAD Capture CIS. A PCB design is soon to follow. This schematic was made partially as a visual demonstration and therefore features components that will not be part of the pcb, such as buttons, which will be panel-mounted.




  • mbenkerumass 10:00 am on November 29, 2019 Permalink | Reply
    Tags: Filters,   

    Microstrip Coupled Line Bandpass Filter 

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

    Microstrip Coupled Line Bandpass Filter





    Final Results:




  • mbenkerumass 10:09 am on November 28, 2019 Permalink | Reply
    Tags: Diodes, Electrical Theory   

    Negative Resistance 

    RF/Photonics Lab
    November 2019
    Jared Alves

    Negative Resistance

    Arguably the most fundamental equation in electrical engineering is Ohm’s Law (V = I*R) which states that voltage is proportional to the product of current and resistance. From this equation, it is apparent that increasing a voltage across an element will increase the current through that element assuming the resistance is fixed. With a resistor, electrical energy is dissipated in the form of thermal energy (heat) due to the voltage drop between the terminals of the device. This is in direct contrast to the concept of negative resistance, which causes electrical power to be produced instead of dissipated.

    Generally, negative resistance refers to negative differential resistance, as negative static resistance is not typically used.  Static resistance is the standard V/I ratio while differential resistance takes the derivative dV/dI. The following image shows an I-V curve with several slopes. The inverse of B yields a static resistance, and the inverse of line C is differential resistance (both evaluated at the point A). If the differential curve has a negative slope, this indicates negative differential resistance.


    Even when differential resistance is negative, static resistance remains positive. This is because only the AC component of the current flows in the reverse direction. A device would consume DC power but dissipate AC power. This is because the current decreases as the voltage increases, leading to


    A tunnel diode is a semiconductor device that exhibits negative resistance due to a quantum mechanical effect called “tunneling”.

  • mbenkerumass 10:02 am on November 27, 2019 Permalink | Reply
    Tags: , , , RADAR   

    Doppler Effect 

    RF/Photonics Lab
    November 2019
    Michael Benker


    Doppler Effect

                    The Doppler Effect is an important principle in communications, optics, RADAR systems and other systems that deal with the propagation of signals through space. The Doppler Effect can be summarized as the resultant change to a signal’s propagation due to movement either by the source or receiving end of the signal. As the distance between two objects changes, so does the frequency. If, for instance, a signal is being propagated towards an object that is moving towards the source, the returning signal will be of a higher frequency.


    The Doppler Effect is also applied to rotation of an object in optics and RADAR backscatter scenarios. A rotating target of a radar or optical system will return a set of frequencies which reflect the distances of each point on the target. If one side of the target is moving closer while the other side is moving away, there will be both a higher and lower frequency component to the return signal.


  • mbenkerumass 9:59 am on November 26, 2019 Permalink | Reply

    034/100 Loaded Q and External Q 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 4.2-3: Analyze the parallel resonator that is attached to a 50 Ohm source and load as shown.


    This problem is specifically asking to define the Q factor related to this circuit. The Q factor is a ratio of energy stored (by an inductor or capacitor) to the power dissipated in a resistor. The Q factor varies with frequency since the effect of a capacitor or inductor also vary with frequency. For a series resonant circuit, the “unloaded” Q factor is defined by the following function: Qu = X / R = 1/(wRC) = wL/R

    The unloaded Q factor of a parallel resonant circuit: Qu = R / X = R/(wL) = wRC

    Overall, the Q factor is a measure of loss in the resonant circuit. A higher Q corresponds to lower loss, while a lower Q indicated higher loss. An “unloaded” Q factor means that the resonator is not connected to a source or load. The above circuit can no longer apply the “unloaded” Q factor formulas due to the presence of a source and a load. There are two further Q factor formulas that need to be considered: loaded Q factor and external Q factor. The loaded Q factor includes the source resistance and load resistance with the resistance of the circuit. The external Q factor refers to only the source resistance and load resistance together.

    For the above circuit, the loaded Q factor for the parallel resonator is defined as:

    Loaded Q = (Rs + R + Rl)/(wL) = (Source resistance + R + load resistance) / (wL)

    The external Q factor for the source resistance and load resistance is:

    External Q = (Rs + Rl)/(wL) = (Source resistance + load resistance)/(wL)

    The relationship between the different types of Q factors are:

    1/(Loaded Q) = 1/(External Q) + 1/(Unloaded Q)

  • mbenkerumass 11:35 am on November 25, 2019 Permalink | Reply

    033/100 Parallel Resonant Circuits 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 4.2-2: Analyze a rearrangement of the RLC components into a parallel configuration.

    As observable by the following figures, the resonant frequency and impedance value remain the same for the parallel RLC circuit. What may be understood by this is that the reactance of the inductor cancels out the reactance of the capacitor at this frequency of 505 MHz.

    The input admittance of a parallel resonant circuit is: Y = (1/R) + jwC + (1/jwL).

    The angular frequency, w = 2*pi*f = 1 / (sqrt(L*C)).


  • mbenkerumass 9:30 pm on November 24, 2019 Permalink | Reply

    032/100 Series Resonant Circuits 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 4.2-1: Analyze a one port series RLC circuit with R = 10 Ohms, L = 10 nH and C = 10 pF.

    According to the following results, the input impedance at resonance is 10 Ohms, which is the value of the resistor.

    The input impedance of an RLC series circuit is modeled by the following formula, a rather basic expression: Z = R + jwL + 1/(jwC)

    The power delivered to the resonator is: P = |I|^2 * Z / 2.


  • mbenkerumass 5:30 pm on November 23, 2019 Permalink | Reply
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    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 10:08 am on November 22, 2019 Permalink | Reply
    Tags: , Optics,   

    Interferometry – Introduction 

    RF/Photonics Lab
    Jared Alves
    November 2019

    Interferometry – Introduction

                    Interferometry is a family of techniques in which waves are superimposed for measurement purposes. These waves tend to be radio, sound or optical waves. Various measurements can be obtained using interferometry that portray characteristics of the medium through which the waves propagate or properties of the waves themselves. In terms of optics, two light beams can be split to create an interference pattern when the waves combine (superimpose). This superposition can lead to a diminished wave, an increased wave or a wave completely reduced in amplitude. In an easily realizable physical sense, tossing a stone into a pond creates concentric waves that radiate away from where the stone was tossed. If two stones are thrown near each other, their waves would interfere with each other creating the same effect described previously. Constructive interference is the superposition of waves that results in a larger amplitude whereas destructive interference diminishes the resultant amplitude. Normally, the interference is either partially constructive or partially destructive, unless the waves are perfectly out of phase. The following image displays total constructive and destructive interference.


    A simple way to explain the operation of an interferometer is that it converts a phase difference to an intensity. When two waves of the same frequency are added together, the result depends only on the phase difference between them, as explained previously.

    interferrometry2The image above shows a Michelson interferometer which uses two beams of light to measure small displacements, refractive index changes and surface irregularities.  The beams are split using a mirror that is not completely reflective and angled so that one beam is reflected, and one is not. The two beams travel in separate paths which combine to produce interference. Whether the waves combine destructively or constructively depends on distancing between the mirrors. Because the device shows the difference in path lengths, it is a differential device. Generally, one leg length is kept constant for control purposes.

  • mbenkerumass 9:13 pm on November 21, 2019 Permalink | Reply

    023/100 Distributed Bias Feed Design 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 2.11-3: Calculate the physical line length of the λ/4 sections of 80 Ω and 20 Ω microstrip lines at a frequency of 2 GHz. Create a schematic of a distributed bias feed network.

    A high impedance microstrip line of λ/4 can be used to replace the lumped inductor from problem 022/100 Example 2.11-2E. Likewise a quarter wave impedance line of a low impedance can replace the lumped shunt capacitor. The 80 Ohm and 20 Ohm transmission lines can be made using LineCalc at 2 GHz. The taper, tee and end-effect element are used to simulate the circuit most correctly and to remove discontinuities between the models.


    The return loss null occurs at 1.84 GHz, indicating that the system could be optimized better to adjust center frequency. The high impedance line length is now adjusted to center the frequency to 2 GHz:




  • mbenkerumass 8:36 pm on November 20, 2019 Permalink | Reply

    022/100 Microstrip Bias Feed Networks 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 2.11-2E: Design a lumped element biased feed network.

    Bias feed networks are an important application of high impedance and low impedance microstrip transmission lines. The voltage bias may be needed for a device that is connected to the microstrip line, such as a transistor, MMIC amplifier or diode. The inductor in the circuit below is used as an “RF Choke”, which is used in tandem with a shunt or bypass capacitor for a “bias decoupling network.” Lumped elements are typically used for frequencies below 200 MHz.

    The following is a typical bias feed network, followed by a simulation:



  • mbenkerumass 7:45 pm on November 19, 2019 Permalink | Reply

    021/100 Distributed Inductance and Capacitance 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 2.11-2D: Convert the lumped element capacitors and inductors to distributed elements.

    This is the schematic that needs to be changed into distributed element microstrip lines:


    The following formulas are needed to calculate the inductive and capacitive line lengths to simulate this schematic using microstrip lines.

    Inductive line length: (frequency)*(wavelength)*(Inductance)/(impedance of line)

    Capacitive line length: (frequency)*(wavelength)*(Capacitance)*(impedance of line)

    In order to know what at which frequency the inductance or capacitance are calculated, let’s run the simulation of the above circuit:


    This circuit is centered at 10 GHz, since the circuit behaves as a terminated open-circuited transmission line with an open-parallel resonance at 180 degrees, or twice the length of a quarter wave line.

    The above circuit is then modeled as follows:



  • mbenkerumass 4:10 pm on November 18, 2019 Permalink | Reply

    020/100 Open-Circuited Transmission Line with Termination 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 2.11-2C: Calculate the input impedance of a quarter wave open-circuited microstrip transmission line using termination with end effects.

    An open circuit microstrip line generates a capacitive end effect due to radiation. This radiation is observable in the results from the following simulation. Note that the impedance at 180 degrees is more capacitive than was the open circuit transmission line with out any termination.


  • mbenkerumass 2:23 pm on November 17, 2019 Permalink | Reply

    019/100 Open-Circuit Transmission Line 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 2.11-2B: Calculate the input impedance of a quarter wave open-circuited microstrip transmission line for a given length of time.

    The reactance of a lossless open circuit transmission line can be modeled as being equal to the characteristic impedance multiplied by the cotangent of the electrical length of the transmission line in degrees.

    X = Z * cot(Θ)

    To construct this circuit, a termination of 1 MOhms is used to simulate an open circuit. As the electrical length in degrees varies with frequency (the wavelength), a static electrical length of a transmission line varied over many frequencies will suffice to demonstrate the reactance of a varying electrical length transmission line. The following circuit was created with a transmission line optimized for 10 GHz, similar to the Short-circuited Transmission Line:


    The results above are consistent with the theoretical model of an open circuit transmission line being modeled by a cotangent relationship. At the optimized frequency (at which the transmission line length is quarter-wave) it can be observed that the impedance of the line is measured to be zero. At a half-wave length and other multiples of a half wave length, the transmission line generates high levels of resonance.


  • mbenkerumass 1:33 pm on November 16, 2019 Permalink | Reply

    018/100 Short-circuited Transmission Line 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    November 2019
    Michael Benker

    Example 2.11-2A: Calculate the input impedance of a short-circuited microstrip transmission line for a given electrical length of the line.

    This circuit was built with a quarter-wave microstrip synthesized for 10 GHz with given substrate (conductivity of gold) using the LineCalc tool.


    The following results conclude that a short-circuited quarter-wave transmission line has high impedance, similar to an open circuit. A short circuited transmission line that is not a quarter-wave transmission line will not have high impedance as demonstrated by frequencies far outside of the range of optimization (10 GHz). This phenomena is is consistent with electromagnetic theory on transmission lines.


    Theoretical relationship between transmission line length (short-circuited) and it’s imaginary impedance component:



  • mbenkerumass 10:33 pm on November 14, 2019 Permalink | Reply
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    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
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    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
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    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


  • mbenkerumass 10:14 am on November 10, 2019 Permalink | Reply
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    Random Signal Analyzer – MATLAB 

    ECE457 Senior Design
    November 2019
    Michael Benker

    Random Signal Analyzer

    The following MATLAB program is designed to create a random signal and analyze statistical properties. The applications for this are a current senior design project and the code may eventually be implemented in a project that involves a sound level analysis program on a microcontroller.



  • mbenkerumass 4:35 pm on November 9, 2019 Permalink | Reply
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    Angle Modulation 

    RF/Photonics Lab UMASS Dartmouth
    November 2019
    Michael Benker

    Angle Modulation

    In comparison to Amplitude Modulation, which varies the magnitude of the sinusoidal carrier wave, Angle Modulation varies the phase of the carrier wave. The two most common forms of angle modulation are phase modulation (PM) and frequency modulation (FM). Phase modulation varies the instantaneous angle linearly with the message signal, while frequency modulation varies the instantaneous frequency with the message signal. The signals on the right are understood (from top to bottom) as the carrier frequency,the modulating wave and the result signal of amplitude modulation, phase modulated and frequency modulation. Due to phase modulated and frequency modulated waves having constant amplitude AC, noise is expected to be lower, although the transmission bandwidth is increased.Rates of distortion are reduced with a reduced possibility of a polarity shift. The average power for angle modulated wave is Pave=(1/2)*(AC)2.The table below summarizes the relationship between phase-modulated and frequency-modulated waves. An FM wave can be seen as a PM wave with a substitution of the integral of the message signal for the message signal. Further, an FM wave can be represented as having gone through an integrator while a PM wave is represented as having gone through a differentiator.

    The benefits of conserving bandwidth lead to the development of the narrow-band frequency modulation scheme. To achieve this, several parameters are defined. The frequency deviation, or the maximum departure of the instantaneous frequency from the carrier frequency is defined as Δf = kfAm, where kf (as mentioned in Table 4.1) is the frequency sensitivity factor.The modulation index, β is the ratio of the frequency deviation to the modulation frequency: β = Δf/fm. The angle of the FM wave and the FM wave itself are described as: The following block diagram depicts a method for generating a narrow-band FM wave:Carson’s rule defines an approximate relation for the transmission bandwidth of an FM wave generated by a single-tone modulating wave. From the following expression(Carson’s rule), it is understood that large values of the modulation index β the bandwidth is slightly greater than the twice the frequency deviation Δf and for small values of the modulation index, the spectrum is limited to the carrier frequency and a pair of side-frequencies at fc± fm, in which case the bandwidth approached 2*fm.



    • Jared 11:28 pm on November 9, 2019 Permalink | Reply

      Phase modulation is a bit tougher to understand for me than frequency modulation. Awesome post


      • mbenkerumass 5:59 am on November 10, 2019 Permalink | Reply

        For phase modulation, I think one way to understand it is to think of the effects we talk about using transmission lines. Depending on the length of the line in comparison to the wavelength, there is a phase shift on the output. This is a type of phase modulation. It would be interesting to ask Dr. Gendron about that one.


  • mbenkerumass 5:46 pm on November 8, 2019 Permalink | Reply

    Fiber Optics (Introduction) 

    RF/Photonics Lab at UMASS Dartmouth
    November 2019
    Michael Benker

    Fiber Optics

    When the frequency of a signal is increased, so does the transfer rate. On the electromagnetic spectrum, light waves occupy frequency ranges of several hundred Terahertz. Fiber optics and photonics take advantage of the speed of light waves to allow for a different approach to data communications. When using light waves instead of electrical charges, this drastically alters the normal characteristics of electrical information transfer. A light wave being sent through glass in a fiber optic wire is no longer restricted to Ohm’s law for example, since a light wave will move through a resistor without any loss. Although light waves are susceptible to quantum noise, they are immune to noise caused by heat (in many cases, this means they are virtually noise-less). Fiber optics, due to their high data rates, flexibility and immunity to noise offer an extraordinary opportunity for scientific and engineering progress.


  • mbenkerumass 7:21 pm on November 7, 2019 Permalink | Reply
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    Rat Race Coupler: ADS 

    ECE435 – RF/Microwave Engineering, Professor Dr. Yifei Li
    November 2019
    Michael Benker
    Rat Race Coupler ADS Simulation





  • mbenkerumass 7:11 pm on November 6, 2019 Permalink | Reply
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    Frequency Shift Keying 

    ECE471 – Communication Theory, Professor Dr. Paul Gendron
    November 2019
    Michael Benker
    Frequency Shift Keying


    The following MATLAB code simulates Frequency Shift Keying, an essential part of Communications.





  • mbenkerumass 4:17 pm on October 30, 2019 Permalink | Reply
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    Directional Coupler ADS Simulation 

    ECE435 – RF/Microwave Engineering, Professor Dr. Yifei Li
    October 2019
    Michael Benker
    Directional Coupler ADS Simulation




  • mbenkerumass 10:39 am on October 26, 2019 Permalink | Reply
    Tags: HFSS, RCS   

    HFSS RCS Backscatter Analysis 

    RF/Photonics Lab UMASS Dartmouth, Advisor Dr. Yifei Li
    October 2019
    Michael Benker
    HFSS RCS Backscatter

    Below is an RCS backscatter simulation of a cylinder up to 100 GHz. The main goal of this task was to gain a comfort level using HFSS to perform further RCS backscatter simulations in the future. Using HFSS has been interesting, especially due to the amount of computing strength it may require at times. I look forward to using this program more in the future.

    Attached is also a PDF guide (not my own) that can be useful for performing a similar simulation: Getting_Started_with_HFSS





  • mbenkerumass 10:20 pm on October 22, 2019 Permalink | Reply
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    MATLAB Data Analysis – Senior Design Project Component 

    ECE457 – Senior Design Project, Professor Dr. Fortier
    October 2019
    Michael Benker
    MATLAB Data Analysis


    The following code was one component of my current Senior Design Project assignment, which will involve the creation of a device known as the “Audio Awareness Enabler.” More information relating to this project is sure to follow in the future. For now, let us take a look at the following MATLAB code, which takes excel files of data and calculates the averages and standard deviations and then plots a Gaussian normal plot. Soon, this code will be modified to be able to determine whether a set of data will fall into the “ambient” range or one of the three interrupt levels. It will also eventually seek to create a formula that will determine whether a set of data is in the interrupt zone based on the ambient level.

    See the pdf file: ece457p9v002


    Data at one location:


    Next location:


  • mbenkerumass 7:11 am on October 18, 2019 Permalink | Reply
    Tags: , ,   

    ADS Coupler Momentum Simulation 

    ECE435 – RF/Microwave Engineering, Professor Dr. Yifei Li
    October 2019
    Michael Benker
    ADS Coupler Momentum Simulation

    Build the ADS circuit.


    Run the momentum simulation and set parameters such as substrate.


    This is a momentum simulation. Let’s see if we can optimize this.


    Export the part to be used as a component in the workspace library in ADS.


    Now run an ADS simulation using the exported component, which uses a database of simulated results.


    If you step into the component, you will see component features.


    Now, tune the parameters to begin optimization.


  • mbenkerumass 8:43 pm on October 12, 2019 Permalink | Reply

    NanoVNA – Handheld Vector Network Analyzer 50kHz-900MHz 

    A Network Analyzer for $60 on Amazon. Looking forward to owning my own and spending more time with Network Analyzers, like the one’s in the RF/Photonics Lab.


  • mbenkerumass 6:19 pm on October 11, 2019 Permalink | Reply
    Tags: , , , Research,   

    RCS/ISAR Data Acquisition (testing Demodulator) 

    RF/Photonics Lab at UMASS Dartmouth, Advisor: Professor Dr. Yifei Li
    October 2019
    Michael Benker
    RCS/ISAR Data Acquisition

    The following MATLAB program utilizes a set of data acquired using an oscilloscope to test a demodulator. This is part of a project being undertaken at the UMASS Dartmouth RF/Photonics Lab. To view a published version of the code: rcs20190925.


  • mbenkerumass 10:28 pm on October 10, 2019 Permalink | Reply
    Tags: , ,   

    Branchline Coupler – EM Simulation 

    ECE435 – RF/Microwave Engineering, Professor Dr. Yifei Li
    October 2019
    Michael Benker
    ADS Momentum Simulation



  • mbenkerumass 12:48 am on October 9, 2019 Permalink | Reply
    Tags: , ,   

    MATLAB Simulation: Voltage Control Oscillator 

    ECE471 – Communication Theory, Professor Dr. Paul Gendron
    October 2019
    Michael Benker
    Voltage Control Oscillator MATLAB Simulation, Integral to Costa’s Receiver


  • mbenkerumass 10:19 pm on October 8, 2019 Permalink | Reply
    Tags: ,   

    ADS Momentum Simulation 

    ECE435 – RF/Microwave Engineering, Professor Dr. Yifei Li
    October 2019
    Michael Benker
    ADS Momentum Simulation



  • mbenkerumass 12:41 am on October 4, 2019 Permalink | Reply
    Tags: ,   

    Quadrature Hybrid Coupler 

    ECE435 – RF/Microwave Engineering, Professor Dr. Yifei Li
    October 2019
    Michael Benker
    Project 4 – Quadrature Hybrid Coupler

    Presentation: Project4_presentation



  • mbenkerumass 1:30 am on September 17, 2019 Permalink | Reply
    Tags: ,   

    Smith Chart Impedance Matching 

    ECE435 – RF/Microwave Engineering, Professor Dr. Yifei Li
    September 2019
    Michael Benker
    Project 1 – Smith Chart Impedance Matching

    Presentation: proj1_presentationproj1_schematic



  • mbenkerumass 8:26 pm on June 29, 2019 Permalink | Reply

    016/100 Example 2.9-1 Waveguide Insertion Loss 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 2.9-1: Consider the model of a one inch and a three inch length of the waveguide as used in an X Band satellite transmission system. Display the insertion loss of the waveguides from 4 to 8 GHz.

    377 Ohms simulates free space


  • mbenkerumass 7:10 pm on June 27, 2019 Permalink | Reply

    014/100 Example 2.4-1 VSWR Measurement of Series RLC 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    October 2019
    Michael Benker
    Example 2.4-1: For series RLC elements, measure the reflection coefficients and VSWR from 100 to 1000 MHz in 100 MHz steps.


  • mbenkerumass 4:45 pm on June 26, 2019 Permalink | Reply

    013/100 Example 1.5-2B Physical Capacitor Q Factor versus Frequency 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    October 2019
    Michael Benker
    Example 1.5-2B: Calculate the Q factor versus frequency for the modified physical model of an 8.2 pF multilayer chip capacitor.



  • mbenkerumass 4:30 pm on June 25, 2019 Permalink | Reply

    012/100 Example 1.5-2A Dissipation Factor in Capacitor 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.5-2A: Calculate the Q factor versus frequency for the physical model of an 8.2 pF multilayer chip capacitor.


  • mbenkerumass 4:12 pm on June 24, 2019 Permalink | Reply

    011/100 Example 1.5-1 Single Layer Capacitor 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.5-1 Consider the design of a single layer capacitor from a dielectric that is 0.010 inches thick and has a dielectric constant of three. Each plate is cut to 0.040 inches square. Calculate the capacitor value and its Q factor.

    Capacitance formed by a dielectric material between two parallel plate conductors:

    C = (N-1)(KAεr/t)(FF) pF

    A: plate area
    εr: relative dielectric constant
    t: separation
    K: unit conversion factor; 0.885 for cm, 0.225 for inches
    FF: fringing factor; 1.2 when mounted on microstrip
    N: number of parallel plates



  • mbenkerumass 3:49 pm on June 23, 2019 Permalink | Reply

    010/100 Example 1.4-6 Magnetic Core Inductors 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.4-6 Design a 550 nH inductor using the Carbonyl W core of size T30/ Determine the number of turns and model the inductor in ADS.

    Number of turns calculation: N = sqrt(L/A) = sqrt(55nH/2.5) = 14.8




  • mbenkerumass 1:09 pm on June 21, 2019 Permalink | Reply

    008/100 Example 1.4-4 Q Factor of Air Core Inductor 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.4-4 Calculate the Q factor of the air core inductor used in previous example 1.4-2.


  • mbenkerumass 12:57 pm on June 20, 2019 Permalink | Reply

    007/100 Example 1.4-3 Air Core Inductor Equivalent Network 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.4-3 Create a simple RLC network that gives an equivalent impedance response similar to previous example 1.4-2.


  • mbenkerumass 12:33 pm on June 19, 2019 Permalink | Reply

    006/100 Example 1.4-2 Air Core Inductor 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.4-2 Calculate and plot the input impedance of an air core inductor.



  • mbenkerumass 12:05 pm on June 17, 2019 Permalink | Reply

    004/100 Example 1.3-1B Parasitic Elements of a Physical Resistor vs. Frequency 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.3-1B: Plot the impedance of a 5 Ω leaded resistor in ADS over a frequency range of 0 to 2 GHz.


    This indicates a resonance at 500 MHz. This is due to the parasitic iductance and capacitance that exists on a real resistor. The resistor behaves as a combination of series parasitic inductance and resistance, in parallel with a parasitic capacitance.

    The impedance of an inductor is reduced as the frequency increases, while the impedance of a capacitor increases as the frequency increases. The intersection frequency of these two patters meet is the resonant frequency.

    The resonance frequency can be found from equating XL and XC. The formula is:

    Resonant frequency fR = 1/(2*pi*sqrt(LC))

  • mbenkerumass 11:47 am on June 16, 2019 Permalink | Reply

    003/100 Example 1.3-1A Ideal Resistors 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.3-1A Plot the impedance of a 50 Ω ideal resistor in ADS over a frequency range of 0 to 2 GHz.


    Thereby noting that an ideal resistor maintains constant impedance with respect to frequency.

    You were here and you read it, so don’t forget it.


  • mbenkerumass 3:30 pm on June 15, 2019 Permalink | Reply

    002/100 Example 1.2-4 Skin Effect and Flat Ribbons 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.2-4 Calculate the inductance of the 3 inch Ribbon at 60 Hz, 500 MHz, and 1 GHz. Make the ribbon 100 mils wide and 2 mils thick.


    The flat ribbon inductance is calculated with the following equation:

    L = K*l*[ ln((2*l)/(W+T))+0.223*(W+T)/l + 0.5 ] nH

    l: length of the wire
    K: 2 for dimensions in cm and K=5.08 for dimensions in inches
    W: the width of the conductor
    T: the thickness of conductor


  • mbenkerumass 3:15 pm on June 14, 2019 Permalink | Reply

    001/100 Example 1.2-1 Reactance and Inductance with respect to Frequency 

    100 ADS Design Examples Based on the Textbook: RF and Microwave Circuit Design
    Michael Benker
    Example 1.2-1: Calculate the reactance and inductance of a three inch length of AWG #28 copper wire in free space at 60 Hz, 500 MHz, and 1 GHz.



    > The increase in reactance with respect to frequency represents the skin effect property, in which, as the frequency increases, the current density begins to be concentrated on the surface of a conductor.

  • mbenkerumass 11:12 pm on June 13, 2019 Permalink | Reply

    100 ADS Design Examples, RF and Microwave Circuit Design 

    I found this book has a number of interesting problems that I would like to go through by myself to get some experience with ADS. I may change my mind, however I intend on posting my solutions to my blog (here) as I go through them, if I do. Stay tuned.


  • mbenkerumass 4:58 pm on May 26, 2019 Permalink | Reply
    Tags: ,   

    OrCAD Tutorial/Study Guide 

    This post outlines the steps needed to create a schematic using OrCAD and then prepare it for manufacture as a PCB board. Writing this post helps me to learn OrCAD better and this will serve as a guide for review later. I will be using the free version, OrCAD Lite.


    Opening a new project

    1. First, start a new project.



    2. Give the project a name and create the folder that you want for the project files. Select PSpice Analog or Mixed A/D.



    3. Select “Create a blank project” if starting from scratch.



    Building the Schematic

    4. Select the “Place Part” button or press P to open the parts menu.



    5. This next part requires a bit of knowledge about where which libraries the components are found under. Here, I want to place a resistor, so I typed R and selected the library “Analog”. If the libraries are not added, you can find them in the OrCAD folder on the PC and add them using the “Add libraries” button shown on the screen.



    6. Double-click on the part in the menu to place it on the schematic page. I also added a VDC, which is found in the Source library. Finish placing parts.



    7. In this case, I will add an LED, but I am unable to find it in the Place Part menu. To find what I am looking for, I chose “Place”, “PSpice Component…” and “Search…” to open a new menu shown below. Further components can be found here if you are unable to find what you need. Under part name and description, select one from the list to add it to the schematic.



    8. Press G on the keyboard to add a ground. I chose “0/CAPSYM”. Now select the “Place Wire” button or W to put down the wires.



    9. Double-click on the voltage and resistor values to change them as necessary.




    10. To run a simulation, on the drop down menu, select “PSpice”, “New Simulation Profile”. Give this simulation a name.




    11. Define the parameters for this simulation, click apply and Ok.



    12. Select the voltage probe and add it to the circuit.



    13. Select “Run” and open the new simulation window to view results.




    PCB Design

    14. First, a folder will be created for the PCB. Rename the schematic folder in the main project folder., then rename the default “PAGE1” page name.




    15. Right-click on the main project folder and create a new schematic. This will be for the PCB board. Now, copy the schematic from the schematic folder and paste it to the new PCB folder. Rename the copied schematic to indicate it is for PCB and not the schematic.





    16. Make the PCB folder the root folder. Click and open the PCB schematic file.



    17. For the PCB board, the DC voltage needs to be replaced with connectors. Select the VDC and delete it. Select “Place Part” and choose to add a new library. The connectors are found in the library folder shown below.





    18. Select CON1 from the part list and place the parts where the VDC was connected. Remember to save.



    19. Select all the components and go to “Edit”, “Properties”.  Select the “Parts” tab on the lower left.




    20. Scroll to the right to view the PCB Footprint tab. The footprint names here are then changed to the footprint names found in the libraries. Save.



    21. Now, open the OrCAD PCB Designer program and create a new drawing in the main project folder. I put it in a separate folder inside the project folder. Selecting the board wizard will take you through a series of prompts.



    22. Continue through the wizard (in this case using only default settings until Spacing Constraints). At Spacing Constraints, change the Minimum line width from the default 0 (this default setting can be problematic). Then select the default via padstack. I chose “Via”. Select ok. Continue through the wizard. In this case, choose a rectangular board. After finishing the wizard, you will see an empty square. Now, save and close the PCB designer.




    23. Go back to Capture CIS, open the project tab and select the PCB schematic file. Select “Tools”, “Create Netlist…” to begin transferring the schematic to a printed circuit board. Select Create of Update PCB Editor Board and choose the file created using OrCAD PCB Designer. For the output file, I chose to output the board to the same file, since I won’t be needing the empty board file. Now, select Open Board in OrCAD PCB Editor and select OK.




    24. Now, go to “Place”, “Components Manually…” to add the parts from the schematic to the PCB. Select the components you need to place (or select all if you will place all of them) and hide the menu.




    25. Place the parts on the board. Parts may need to be rearranged to fit nicely. When satisfied,, right-click and select “Done”. Save and “overwrite”.



    26. Now select in the menu, “Route”, “Connect” to place wires connecting the components. When finished, right-click and select “Done”. Once again, save and “overwrite”.




    Generating Gerber and Drill files and Online Check


  • mbenkerumass 4:50 am on April 30, 2019 Permalink | Reply
    Tags: Analog Electronics, Multisim   

    Differential Amplifier 

    This lab demonstrates the rejection of common-mode noise while amplifying differential-mode signals. This is the final circuit in Multisim.


    The circuit is comprised of one oscillator, one inverting amplifier, two weighted summers and one differential amplifier.

    This is a screen capture of the noise disconnected.



  • mbenkerumass 2:40 am on April 30, 2019 Permalink | Reply
    Tags: ,   

    20 GHz RF Amplifier Design – ADS 

    ECE336 – Electromagnetic Theory II, Professor Dr. Yifei Li
    April 2019
    Michael Benker
    20 GHz RF Amplifier Design – ADS

    This is a 20 GHz amplifier circuit, made using smith chart impedance matching in ADS. This circuit is one of the first times I have used this powerful software. Glad to be putting my emag theory to work to build something real. The report should be helpful for me to jog my memory to do it again. With the notes I have, a similar circuit should be possible.

    For the impedance matching, I considered using an inductor, though using only caps and t-lines, the result seemed to be cleaner.



    See the following for the full report:


  • mbenkerumass 1:21 pm on April 27, 2019 Permalink | Reply
    Tags: C, Embedded Systems Design   

    Digital Alarm Clock 

    Digital Alarm Clock Project – Embedded Systems Design

    See full report:

    Lab Report 5 – Digital Alarm Clock

    Digital Alarm Clock User Manual

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