Tag Archives: 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.

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

 

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.

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.

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

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

 

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

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

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

 

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

 

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

input.png

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.

schem.PNG

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.

results

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.

ocschem

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.

oc

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.

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.

ads_1.PNG

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.

schematic.PNG

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.

res

The following image demonstrates placing equations in the data display window and using a calculated value to compare with a simulated value.

eqn

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.

measured

 

 

 

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.

isolator.jpg

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.

stub.png