Tagged: Microwave/RF Engineering Toggle Comment Threads | Keyboard Shortcuts

  • jalves61 6:00 am on May 28, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Mathematical Formulation for Antennas: Radiation Integrals and Auxiliary Potentials 

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

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

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

    cfr

    And also the identity:

    1

    It can be shown that:

    2

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

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

    3

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

    4

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

    5

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

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

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

    mxw

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

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

     

     
  • jalves61 6:00 am on May 19, 2020 Permalink | Reply
    Tags: Microwave/RF Engineering   

    The Cavity Magnetron 

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

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

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

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

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

    unnamed

     

     
  • jalves61 4:04 am on April 30, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    The Half Wave Dipole Antenna 

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

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

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

    regions

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

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

    patterns

     

     
  • jalves61 6:55 am on April 24, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering,   

    The Radar Range Equation 

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

    1

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

    2

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

    3

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

    4

    5

    6

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

    7

     
  • jalves61 12:48 am on April 18, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering,   

    Yagi-Uda Antenna/Parasitic Array 

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

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

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

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

    yagi

     
  • jalves61 7:52 pm on April 15, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Miller Effect 

    The Miller Effect is a generally negative consequence of broadband circuitry due to the fact that bandwidth is reduced when capacitance increases. The Miller effect is common to inverting amplifiers with negative gain. Miller capacitance can also limit the gain of a transistor due to transistors’ parasitic capacitance. A common way to mitigate the Miller Effect, which causes an increase in equivalent input capacitance, is to use cascode configuration. The cascode configuration features a two stage amplifier circuit consisting of a common emitter circuit feeding into a common base. Configuring transistors in a particular way to mitigate the Miller Effect can lead to much wider bandwidth. For FET devices, capacitance exists between the electrodes (conductors) which in turn leads to Miller Effect. The Miller capacitance is typically calculated at the input, but for high output impedance applications it is important to note the output capacitance as well.

    cascode

    Interesting note: the Miller effect can be used to create a larger capacitor from a smaller one. So in this way, it can be used for something productive. This can be important for designing integrated circuits, where having large bulky capacitors is not ideal as “real estate” must be conserved.

     
  • jalves61 4:53 pm on April 14, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Beamforming 

    Beamforming (spatial filtering) is a huge part of Fifth Generation wireless technology. Beamforming is basically using multiple antennas and varying the phase and amplitude of the inputs to these antennas. The result is a directed beam in a specific direction. This is a great method of preventing interference by focusing the energy of the antennas. Constructive and Destructive interference is used to channel the energy and increase the antennas’ directivity. The receiver receives the multitude of waves and depending on the receiver’s location will determine whether there is mostly constructive or destructive interference. Beamforming is not only used in RF wireless communication but also in Acoustics and Sonar.

    An important concept to know is that placing multiple radiating elements (antennas) together increases the directivity of the radiation pattern. Putting two antennas side by side, creating a main lobe with a 3dB gain going forward. With four radiating elements, this becomes 6dB (quadruple gain). Feeding all of the elements with the same signal means that the elements are still one single antenna, but with more forward gain. The major issue here is that you only benefit from this in one single stationary direction unless the beam can be moved. This is where feeding the antennas with different phases and amplitudes comes in. The number of antennas becomes equal to the number of input signals. Having more separate antennas (and more input signals) creates a more directed antenna pattern. Spatial multiplexing can also be implemented to service multiple users wirelessly by utilizing space multiple times over.

    Using electronic phase shifters at the input of the antennas can decrease cost of driving the elements quite a bit. This is known as a phased array and can steer the beam pattern as necessary but can only point in one direction at a time.

    phased array

     

     
  • jalves61 1:50 pm on April 13, 2020 Permalink | Reply
    Tags: Microwave/RF Engineering   

    RF Mixer basics 

    Mixers are three port devices that can be active or passive, linear or nonlinear. They are used to modulate (upconvert) or demodulate (downconvert) a signal to change its frequency to be sent to a receiver or to demodulate at the receiving end to a lower frequency.

    mixer

    Two major mixer categories are switching and nonlinear. Nonlinear mixers allow for higher frequency upconversion, but are less prevalent due to their unpredictable performance. In the diagram above, the three ports are shown. The RF signal is the product or sum of the IF (intermediate frequency) and LO (Local Oscillator) signal during upconversion. Due to reciprocity, any mixer can be used for either upconversion or downconversion. For a downconversion mixer, the output is the IF and the RF is fed on the left hand side.

    freqtran

    The above diagram illustrates the concept of frequency translation. In a receiver, the mixer translates the frequency from a higher RF frequency (frequency that the wave propagated wirelessly through air) to a lower Intermediate frequency. The mixer cannot be LTI; it must be either nonlinear or time varying. The mixer is used in conjunction with a filter to select either upper or lower sideband which are the result of the multiplication of two signals with different frequencies. These new frequencies are the sum or difference of the two frequencies at the two input ports.

    In addition to frequency translation during modulation, RF mixers can also be used as phase comparators, such as in phase locked loops.

    To maintain linearity and avoid distortion, the LO input should be roughly 10dB higher than the input RF signal (downconverter). Unfortunately this increases cost and so therein lies the tradeoff between cost and performance.

     
  • jalves61 9:23 pm on March 26, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    RFID – Radio Frequency Identification 

    RFID is an important concept in the modern era. The basic principle of operation is simple: radio waves are sent out from an RF reader to an RFID tag in order to track or identify the object, whether it is a supermarket item, a car, or an Alzheimer patient.

    RFID tags are subdivided into three main categories: Active, passive and semipassive. Active RFID tags employ a battery to power them whereas passive tags utilize the incoming radio wave as a power source. The semipassive tag also employs a battery source, but relies on the RFID reader signal as a return signal. For this reason, the active and semi passive tags have a greater range than the passive type. The passive types are more compact and also cheaper and for this reason are more common than the other two types. The RFID picks up the incoming radio waves with an antenna which then directs the electrical signal to a transponder. Transponders receive RF/Microwaves and transmit a signal of a different frequency. After the transponder is the rectifier circuit, which uses a DC current to charge a capacitor which (for the passive tag) is used to power the device.

    The RFID reader consists of a microcontroller, an RF signal generator and a receiver. Both the transmitter and receiver have an antennas which convert radio waves to electrical currents and vice versa.

    The following table shows frequencies and ranges for the various bands used in RFID

    RFIDtable

    As expected, lower frequencies travel further distances. The lower frequencies tend to be used for the passive type of RFID tags.

    For LF and HF tags, the working principle is inductive coupling whereas with the UHF and Microwave, the principle is electromagnetic coupling. The following image shows inductive coupling.

    inductive coupling

    A transformer is formed between the two coils of the reader and tag. The transformer links the two circuits together through electromagnetic induction. This is also known as near field coupling.

    Far field coupling/radiative coupling uses backscatter by reradiating from the tag to the reader. This depends on the load matching, so changing the load impedance will change the intensity of the return wave. The load condition can be changed according to the data in order for the data to be sent back to the reader. This is known as backscatter modulation.

     
  • jalves61 7:28 pm on March 20, 2020 Permalink | Reply
    Tags: Microwave/RF Engineering   

    Power Amplifiers basics 

    Multistage amplification is used to increase the overall gain of an amplifier chain. The total gain is the product of each stage’s gain. For example, a microphone can be connected to first a small signal amplifier (voltage amplifier), then a power amplifier before being supplied to a speaker or some other load. The PA (large signal amplifier) is the final stage of the amplifier chain and is the most power hungry. The major features of these PAs are it’s efficiency (usually drain efficiency for FET archetypes or Collector efficiency for BJT amplifiers) and impedance matching to the load. The output power of a PA is typically in tens of watts (small signal amplifiers generally output in mW up to 1 Watt maximum).

    “Small signal” transistors are used for small signal amplifiers whereas “power” transistors are used for PAs. Small signal transistors behave linearly whereas power transistors can suffer from nonlinear distortion.

    PAs can be classified based on the operating point (Q point) location. Class A amplifiers have a Q point at the center of the active region. For Class B, the Q point is at the cutoff region. For Class AB, the Q point is between that of class A and class B. For Class C, it is below cutoff.

    A major parameter of a PA is its efficiency. This is the ratio of AC power to DC input power and is generally expressed in a percentage.

    Harmonic distortion of a PA involves the presence of harmonic multiples of the fundamental frequency at the output. A large input signal can cause this type of distortion

     
  • jalves61 4:06 pm on February 26, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Keysight ADS – Microstrip Line Design 

    The goal of the project is to design a 50 ohm microstrip line at an operating frequency of 10 GHz and phase delay of 145 degrees.

     

    The following ADS simulation will be composed of four major parts:

    a) Designing the microstrip lines using two models (I.J. Bahl and D.K. Trivedi model and E. Hammerstad and Jensen model). The insertion loss (S(2,1)) will be plotted over the range of 10 MHz to 30 GHz.

    b) Assuming reasonable dielectric losses, results should be compared to part a

    c) Creation of ideal transmission lines with same parameters compared to part a and b

    d) Showing dispersion on the lossless microstrip line. This is compared to the ideal line.

     

    The LineCalc tool (which uses the Hammerstad and Jensen model) within ADS is used to design the second line with the correct specifications. The first circuit is designed using hand calculated values.

    schem

    The following shows using the LineCalc tool to get the values for the second schematic.

    linecalc

    The simulation is shown below.

    sim.PNG

    A new substrate is created with a loss tangent of .0002 for the second schematic. The simulation results in:

    schem2.PNG

    An ideal transmission line circuit is created and compared with both the lossy and lossless lines.

    IL.PNG

    In order to demonstrate dispersion, the phase velocity must be calculated. As shown by the values compared from 0 GHz to 30 GHz, the phase velocity does not change for the ideal line, but does for the microstrip line.

    PV

     

     
  • jalves61 7:52 pm on February 23, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Keysight ADS – Frequency Dependence of Microstrip Lines 

    The following ADS simulation will demonstrate how the characteristic impedance and effective dielectric constant change with frequency.  In the simulation, a quarter wave section of multi-layer microstrip line is used to demonstrate frequency effects. The result are expected to show that the dielectric constant and the characteristic impedance are inversely related. When the frequency of the electric field increases, the permittivity decreases because the electric dipoles cannot react as quickly. The multi-layer component is used in place of an ideal component because frequency dependence must be demonstrated. An “MLSUBSTRATE2” component is used with the updated dielectric constant and Dielectric loss tangent.

    schem

    For S parameter analysis, two terminated grounds are required. The effective dielectric constant must be solved for by unwrapping the phase of S(2,1). The results show the characteristic impedance (both real and imaginary parts) increasing with frequency and the dielectric constant decreasing.

    results

     
  • jalves61 6:54 pm on February 21, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Keysight ADS – Transient Propagation 

    The following ADS simulation will demonstrate the effects of transients on a transmission line. A rectangular pulse of duration .5 microseconds will be generated and a net voltage vs time will be plotted for a period of .7 microseconds. The circuit has a mismatched load, producing reflections. A time domain reflectometry analysis will prove that the propagating signal voltage steadily increases after the initial time and as time increases, the reflections will eventually die out and leave a steady state response. This is shown with transient analysis.

    schematic.PNG

    The schematic above contains two circuits for the two parts of the rectangular pulse (one with and one without a time delay). The simulated results are shown below.

    res

    A bounce diagram can also be used to convey Time domain reflectometry analysis, as shown below. This diagram is a plot of the voltage/current at the source or load side after each reflection. This is a general diagram and does not apply to the problem.

    bounce.png

     
  • jalves61 5:01 pm on February 18, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Keysight ADS – Conjugate Matching 

    This project will use conjugate matching to match a capacitive load of 50-j40 to a generator of impedance 25+j30. Since the generator impedance is complex, conjugate matching is required to match the network, as opposed to in situations of low frequency where the reactive components are negligible. In the example, an L network is used to match the generator to the load. Theoretically, differentiating the power and setting this equal to zero proves that maximum power is transferred when the resistance of the source and load are equal and the reactive portions are equal and opposite phase shift/sign.

    The first step is to use the impedances given to calculate the actual lumped inductor and capacitor values to use for the network to work at 2 GHz. 25+j30 corresponds to a 25 ohm resistor in series with a 2.387732 nH inductor and 50-j40 corresponds to a 50 ohm resistor in series with a 1.98944 pF capacitor.

    The following shows the schematic with the source, matching network and load.

    schem

    Running the simulation with Data Display equations yields….

    maxpower

    This shows maximum power transfer at the correct frequency of 2 GHz. The next step is to use the Smith Chart tool. A shunt inductor and series capacitor is used to form the L Network. Exact values can be typed in for these to get the impedance value Z = 0.5 +j0.6 which is the normalized equivalent source impedance (divided by 50).

    sc

    With the capacitor and inductor values recorded, these values can be loaded into a separate schematic and compared to the original schematic results.

    Conjugate matching is not achieved with this Smith Chart configuration so there is no peak at 2 GHz.

    power

    Alternatively, the Smith Chart tool can be used from the palette. From this point with the chart icon selected, the network can be created by selecting “Update Smart Component” from the Smith Chart tool window. These results show that it is important to select the proper design network for the specifications for optimal results.

    sc.PNG

     

     
  • jalves61 8:32 pm on February 17, 2020 Permalink | Reply
    Tags: , Microwave/RF Engineering   

    Keysight ADS – Quarter Wave Transformer Matching 

    In ADS, a batch simulation can be implemented to run different load impedance simulations. This function will be used to simulate a quarter wave transformer matching system for various loads (25, 50, 75, 100, 125 and 150 ohms),  The system is used to match a 50 ohm line with an electrical length of 60 degrees at 1 GHz.

    The simulation will demonstrate that an unmatched load will generate a constant VSWR at all frequencies. With the implementation of the matching network, the VSWR varies because it is only designed to match the network at a specific frequency. A previous post derived the relationship to find the impedance of a quarter wave matching transformer.

    schem

    The VSWR can be plotted by adding equations into the data display window and manually adding equations into the plot window to plot VSWR against frequency for both the matched circuit and the unmatched circuit. The mismatched circuits appears constant over frequency with a very high SWR, as it does not have the matching transformer. The quarter wave transformer is shown to provide excellent matching at specific frequencies.

    VSWR.PNG

    For batch simulations, a slider tool can be implemented to show only specific impedances. Clicking on the axes and changing the names to include the index will update the plot with the specific impedances one at a time. The plot is updated to match the slider value for the load impedance.

    update.PNG

    With the axes correctly updated, sliding the slider tool will change the plot automatically. Also in the data display window, tables can be added to view specific values at different frequencies.

    table.PNG

     

     
c
Compose new post
j
Next post/Next comment
k
Previous post/Previous comment
r
Reply
e
Edit
o
Show/Hide comments
t
Go to top
l
Go to login
h
Show/Hide help
shift + esc
Cancel