# IMD3: Third Order Intermodulation Distortion

We’ll begin a discussion on the topic of analog system quality. How do we measure how well an analog system works? One over-simplistic answer is to say that power gain determines how well a system operates. This is not sufficient. Instead, we must analyze the system to determine how well it works as intended, which may include the gain of the fundamental signal. Whether it is an audio amplifier, acoustic transducers, a wireless communication system or optical link, the desired signal (either transmitted or received) needs to be distinguishable from the system noise. Noise, although situationally problematic can usually be averaged out. The presence of other signals are not however. This begs the question, which other signals could we be speaking of, if there is supposed to be only one signal? The answer is that the fundamental signal also comes with second order, third order, fourth order and higher order distortion harmonic and intermodulation signals, which may not be averaged from noise. Consider the following plot:

We usually talk about Third Order Intermodulation Distortion or IMD3 in such systems primarily. Unlike the second and fourth order, the Third Order Intermodulation products are found in the same spectral region as the first order fundamental signals. Second and fourth order distortion can be filtered out using a bandpass filter for the in-band region. Note that the fifth order intermodulation distortion and seventh order intermodulation distortion can also cause an issue in-band, although these signals are usually much weaker.

Consider the use of a radar system. If a return signal is expected in a certain band, we need to be able to distinguish between the actual return and differentiate this from IMD3, else we may not be able to trust our result. We will discuss next how IMD3 is avoided.

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: 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. 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: 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:   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. # 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 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. 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.

# 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. # 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.

anglemodulation        # 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.  inclass20191105

# 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 