# 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. 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. # 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. 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. 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. # Acoustics and Sound: Beating

Beating is a very important concept in musical instruments. This tremolo-like variation in sound intensity occurs when two pure tones of slightly different frequencies are sounded simultaneously. An experiment can be performed with two tuning forks (one regular and one wrapped with tight rubber bands on the prongs) struck at the same time. The resultant sound intensity will vary, rising and falling periodically. When the sound wave arrives at the ear, the waves initially appear out of phase (destructive interference) then appear in phase (constructive interference). The superposition of the two waves is shown to have a pulsation effect. The frequency of the pulsations is determined by the beat frequency, which is the difference in frequency of the pure tones. The pitch perceived by the ear is the average of the two pure tones. A demonstration can be done with two pipes in an organ (one adjustable pipe). The adjustable pipe is varied within a certain range of the other pipe’s frequency. If the second pure tone is greater than approximately 15 Hz away from the first tone, beating is no longer heard.

# 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. Running the simulation with Data Display equations yields…. 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). 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. 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. # 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. 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. 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. 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. # Acoustic and Electromagnetic Waves – Problems (Part I)     # ARRL Examination Study (Part II)

For part II of the ARRL examination study, we will study propagation of radio waves.

Radio waves spread out when transmitted from an antenna in straight lines unless they are reflected or refracted by some object. Due to this spreading and scattering, the waves become weaker as they propagate farther into the air. This limits the “range” a radio transmission can communicate over. The curvature of the Earth creates a “radio horizon” that limits the range of radio propagation. “Line of sight” propagation is when radio waves are transmitted within direct sight of the receiver. This is commonly done in VHF frequencies and higher. Lower frequencies travel as “ground waves”.

Radio waves are partially reflected when the medium through which the wave propagates changes due to a change in intrinsic impedance (a property defined by permittivity and permeability). Radio waves can even be reflected by change in weather patterns. The figure below shows the concept of diffraction (bending past an obstruction) of radio waves. Diffraction can also refer to spreading when a wave travels through a narrow medium into an open area. Light waves also bend by “refraction” which is exactly how radio waves travel around the earth. The earth is curved and therefore the waves need to bend to propagate past “line of sight” distances. The shorter the wavelength (and hence higher frequency), the easier the wave can travel in and out of buildings by penetration of openings in solid objects.

It interesting to note that different waves received by an antenna can interfere if they are out of phase (destructive interference). This is called “multipath” which is when antennas receive waves from different paths. Moving an antenna a few feet can counterract this. Multipath propagation results in irregular fading. VHF and UHF signals propagating with multipath propagation experience fluttering or “picket-fencing” which comes from rapid variation of the signal strength. Tropospheric propagation or “tropo” is propagation of VHF or higher frequencies assisted by atmospheric phenomena such as weather fronts or temperature inversions. It is not uncommon for Tropo signals to propagate over 300 miles. Reflections can also be caused by conductors such as airplanes. Satellites reflect waves with conductive plating. Thirty to 260 miles above the earth, the ionospheric layer resides. Atoms of nitrogen and oxygen are ionized by UV rays from the sun and become positively charged. The separation of the electrons and the creation of positive ions creates a weakly conductive region. The ionosphere is composed of many different regions. The E, F1 and F2 layers tend to reflect radio waves and the D and E regions tend to absorb waves.

“Skip” or sky wave propagation is when HF waves are completely bent back towards the earth. The conductive surface of the earth reflects the wave back and the process repeats. These “hops” or reflections allow the waves to be received at farther distances. Lower frequencies are bent more than higher frequencies. For this reason, UHF signals are rarely heard beyond the radio horizon. The MUF (maximum usable frequency) and LUF (lowest usable frequency) are the highest and lowest frequencies that can be reflected by the ionosphere without absorption. When sunspot activity increases, the makes the ionosphere more conductive and increases the MUF.

Sporadic or “E-Skip” propagation is when patches of the ionosphere become ionized enough to reflect frequencies as high as VHF and UHF. This is most common during early summer and mid winter months.

# Keysight ADS – Short Circuit Terminated Ideal Transmission Line

Using ADS, a parameter sweep can be used to confirm the results of a short circuited transmission line. The input impedance of a transmission line is given as When the line is terminated by a short circuit, ZL = 0 and the equation reduces to only the imaginary part of the numerator. For integer multiples of the wavelength, the input impedance is equal to zero. At odd multiples of a quarter wavelength, the input impedance becomes infinite and looks like an open circuit.

The following circuit is constructed to test the results. A parameter sweep with the variable theta (the electrical length) is used. The results are shown below. As expected, the reactance alternates between inductive and capacitive for different electrical length values. The reactance is infinite at quarter wavelength multiples and zero at integer multiples of the wavelength. The current is shown to be lagging the voltage by 90 degrees. The major conclusion to be made is that a transmission line does not behave like a lumped element circuit because voltages and currents are different at different lengths along the line. # Keysight ADS – Open Circuit Analysis

Expanding upon the previous project, open circuit analysis can be used to find equivalent per unit length capacitance and conductance values for the dielectric part of the transmission line. The same process is used for the open circuit analysis with new equations for capacitance and conductance. The calculated values from the simulation window are compared to the simulated values from the AC analysis. # Keysight ADS – Extraction of Lumped Element Model from Coaxial Line using Short Circuit Analysis

The following ADS project is meant to analyze an RG58 coaxial cable and extract a “lumped element model” containing discrete components intended to represent distributed values. The lumped element values for R, L, G, and C for ideal coaxial lines can be obtained from the following equations. “a” is the radius of the inner conductor and “b” is the radius of the outer conductor. It is important to note that since these are ideal values, the actual simulation will differ from calculated values. R and G are nonreactive and therefore will be quite similar, however C and L which are frequency dependent will vary.

Like with other ADS projects, creating variables is an easy way to change component values, especially when these need to be duplicated. In the ideal transmission line palette, the COAX_MDS component can be found.

The Dielectric loss model can be changed to Frequency independent, as shown. This will prevent the frequency dependent parameters from changing from the calculated values. First, a short circuit analysis can be performed in order to determine resistance and inductance values (shorting out the dielectric parameters C and G). Using the “name” option at the top of the screen, the input wire can be named “Z_SC”.  An AC simulation can be performed with the schematic shown. The results for per unit length resistance are shown from the simulation. Decibel scale is used for the x axis and the y limits are changed to get a better looking plot. The following image demonstrates placing equations in the data display window and using a calculated value to compare with a simulated value. As expected, the results of the calculated and simulated values agree (they are both close to zero). Although, the resistance differs a bit (not sure why). The inductance normally would vary, but because the frequency independent model was selected for the coax cable, they are exactly the same at 100MHz. # Ferrimagnetic Materials – Circulators and Isolators and Ferrite Phase Shifters

When designing microwave and RF components, a non reciprocal device can be obtained by using ferrimagnetic components. Sometimes, it is a good thing for a device to be reciprocal (when the ports of the S parameter matrix are reversible), but in the case of RF devices such as circulators or isolators, it is important for power flow to only move in one direction or to have directional dependence. When directional dependence is present, permeability and permittivity become a tensor rather than a constant and the material is said to be anisotropic.

Ferrimagnets are different than ferromagnets such as iron or steel in the sense that ferrimagnets have high resistivity and directional dependence at mictrowave frequencies. Both are very strongly magnetic.

A circulator is a three port device which can be matched at all ports and lossless at the same time. It can couple power in direction or the other, but not both directions. If the reverse direction is desired, the Scattering matrix can be transposed. For a ferrimagnetic circulator this is achieved by changing the polarity of the magnetic bias field. Most of the time a permanent magnet is used, but an electromagnetic can be used for the circulator to function as an SPDT switch.

An isolator is a two port device which only functions in a single direction. The scattering matrix shown below, implies that the device is nonreciprocal (asymmetric matrix) and lossy due to disobedience to the unitary matrix properties. An isolator can prevent damage to a high power source by forcing the power to flow only from the source to load. Any reflected power due to an impedance mismatch will be absorbed by the isolator.  The two main types of ferrite isolators are resonance and field displacement isolators.

Another two port nonreciprocal RF device is the ferrite phase shifters. Phase shifters are generally used in test and measurement systems or in phased array antennas where the antenna beam can be steered using the device. It is also possible to design a reciprocal phase shifter. In fact most phase shifters are reciprocal in the sense that they provide an equal phase shift in both directions.

# Impedance Matching – Single Stub Tuning

One way to avoid impedance matching a transmission line to a load with lumped circuit elements is to implement Stub matching. Stubs are sections of transmission line that are terminated by either an open circuit or a short circuit. They can be connected in series or in parallel to the transmission line a certain distance from the load. For microstrip and stripline circuits, parallel configurations are preferred whereas series configurations are preferred for slotline or coplanar waveguides.

Two variables when designing a stub are: the reactance of the stub and the distance between the stub and the load. The idea is that at a specific distance, the susceptance or (reciprocally) the reactance of the load should be cancelled out by the stub. This leads to the cancellation of reflection from the load. This reactance/susceptance value is determine by the length of the stub. The difference in length between a short and open stub is a quarter of the wavelength (which can be confirmed by the Smith Chart).

The Smith Chart can be used to identify the length required for the stub admittance to equal 1+jb by traveling from the right hand side of the chart clockwise until the reactive parts are equal and opposite. You can also draw an SWR circle using the load impedance/admittance and find where the circle intersects the 1+jb circle. Then the same process for finding the stub length can be used. On a Smith Chart, lengths are always a function of the wavelength. # 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.

# 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. # The Human Ear

The Human ear is important to the study of acoustics because it is inborn pressure sensor. It is one of the most sensitive parts of the human body and its job is to sense pressure changes in air and convert these to electrical signals that the brain can process as “sound”. Humans can hear roughly between 20 Hz to 20 kHz but this range decreases with age. The human ear can sense sound intensities from 1 W/sqm to 1 trillionth of a W/sqm. What most people intuitively perceive as music loudness, pitch and timbre roughly corresponds to amplitude (or sound intensity, which is proportional to the square of amplitude), frequency and waveform shape. Of course, these are not one to one relationships because if a tone is too high in frequency (ultrasound) or too low (infrasound) it will effect the perceived loudness because it will not be heard at all, for example.

The human ear consists of three main parts: inner ear, middle ear and outer ear. The outer ear consists of the pinna, auditory canal and eardrum. The pinna (the only visible part of the ear) serves as a guide to guide pressure waves into the ear canal. The ear canal is filled with air which is necessary because sound needs a medium such as air to transmit pressure waves. The waves reach the conically shaped eardrum, which vibrates and sends signals to the brain to process. The middle ear consists of several dense bones (ossicles) called the hammer, anvil and stirrup. These are elastically connected and serve to transmit and amplify sound from the outer to inner ear. These bones are necessary because the pressure waves are being transferred to a different medium (air to ear fluid called endolymph) and require an impedance matching network to transmit sound effectively. This is not unlike the soundboard of a guitar (for impedance matching to air) or an electrical impedance matching network design for maximum power transfer from a source to a load.

The inner ear contains the cochlea and the semicircular canals. The cochlea contains thousands of tiny hair cells that are stimulated by the vibrations of sound. The semicircular canals contribute to our sense of balance, but not the sensation of hearing. The inner ear fluid causes the hairs in the cochlea to bend, which are converted to electrical pulses and sent to the brain. These are sent to the auditory nerve and are interpreted as sound.

The following diagram depicts the human ear as a passive electrical circuit using the “impedance analogy”. The eardrum middle ear section is shown to be a transformer to match the outer ear to the middle ear. There could also be another transformer between the middle ear and the cochlea, as stated before. Without going into excruciating detail, it is important to show that the human ear is not all different from an electrical circuit in the sense that it impedance matches and transforms/transduces different forms of energy. 