EE Principles

Essential concepts that took me years to understand

Let's master some important electrical engineering ideas here. Powerpoint of some ideas.

Impedence

As a signal travels down a cable the path is ideally a smooth one with minimal bumps. But when it gets to the load there's a chance that some of the energy will be reflected back down the path. This can happen if there is an abrupt change in the impedance. Changes in conductuctivity, capacitive, and inductive reactance can all contribute to a frequency dependent reflection of signal energy. This is desirable in some cases and not so much in others. See Max Power Transfer below for details.

Balanced Lines

In an electric circuit one can measure the impedence at any part. Between major components exist "transmission lines". If the impedance (relative to ground) on both conductors is the same all the way down the line, it is considered balanced. The benefit is that external noise is induced equally in both lines so common mode rejection is possible.

Signals are often transmitted over balanced connections using the differential mode, meaning the wires carry signals of opposite polarity to each other (for instance, in an XLR connector, pin 2 carries the signal with normal polarity, and pin 3 carries an inverted version of the same signal). Despite popular belief, this arrangement is not necessary for noise rejection. As long as the impedances are balanced, noise will couple equally into the two wires (and be rejected by a differential amplifier), regardless of the signal that is present on them.[2][3] A simple method of driving a balanced line is to inject the signal into the "hot" wire through a known source impedance, and connect the "cold" wire to the signal's local ground reference through an identical impedance. Due to common misconceptions about differential signalling, this is often referred to as a quasi-balanced or impedance-balanced output, though it is, in fact, fully balanced and will reject common-mode interference. Most explanations of balanced lines assume symmetric (antiphase) signals but this is an unfortunate confusion - signal symmetry and balanced lines are quite independent of each other. Essential in a balanced line is matched impedances in the driver, line and receiver. These conditions ensure that external noise affects each leg of the differential line equally and thus appears as a common mode signal that is removed by the receiver. There are balanced drive circuits that have excellent common-mode impedance matching between "legs" but do not provide symmetric signals.[6][7] Symmetric differential signals exist to prevent interference to other circuits - the electromagnetic fields are canceled out by the equal and opposite currents. But they are not necessary for interference rejection from other circuits. Lines carrying symmetric signals (those with equal but opposite voltages to ground on each leg) are often incorrectly referred to as "balanced", but this is actually differential signaling. Balanced lines and differential signaling are often used together, but they are not the same thing. Differential signalling does not make a line balanced, nor does noise rejection in balanced cables require differential signalling. Circuits driving balanced lines must themselves be balanced to maintain the benefits of balance. This may be achieved by transformer coupling or by merely balancing the impedance in each conductor. This advantage is not directly due to differential signaling itself, but to the common practice of transmitting differential signals on balanced lines. Single-ended signals are still resistant to interference if the lines are balanced and terminated by a differential amplifier.

Symmetric Lines

In a transmission line there exist at least two conductors carrying a signal from the source to the load. When the signals are perfectly out-of-phase then the effective radiation at a distance is zero. This helps prevent the line from being the source of noise to other parts of the circuit. Single-ended signals by definition are not symmetric and can radiate!

Network analyzers

Consider a complete circuit with a source and a load. We define this as a "network" and use network analyzers to measure important properties like impedence and bandwidth. A network analyzer typically has two ports S_1 and S_2. Sometimes you only need one port. For testing antenna bandwidth you would hook the antenna up to just S_1 and the analyzer tells you what frequencies are reflected across a band. Voltage standing waves...hmmmm I need to learn more about VSW ratios.

Max Power Transfer

For ideal load/source impedance ratios it depends on the application. Audio circuits contain wavelengths in the conductors that are huge compared to the circuit itself. This and the fact that modern amplifiers have super low output impedances makes efficiency an option. For audio it is usually desired that one "bridges" the source to the load. This puts a greater voltage drop across the load so more power is used by the load relative to the source. This of course means tons of energy reflected back to the source by the load but that's ok because it does not change the efficiency of the operation. RF circuits are different. RF wavelengths are about the size of the circuit and this makes it possible for tons of power to be wasted in reflection and standing waves. For radio circuits one ideally matches the source impedance to the load impedance such that no energy is reflected back. This is needed when noise is an issue.

Sometimes it is important to know the instantaneous phase of a signal in real-time. Coherent systems by definition have well known phases along the transmission line. I-Q modulation is one way of doing this. With this modulation there are two signals, one "In-Phase" carries the raw signal of interest. The second carries the instantaneous phase of the raw signal. This is essentially two signals that are 90 degrees out of phase with eachother, hence quadrature because 360/4 = 90. Many times coherency through out the system is not needed untul post-processing. In this case a Hilbert transform takes any raw signal and generates a complex signal where the imaginary part is the instantaneous phase.

Compressed Sensing

This is the idea that we tend to measure an unecessary amount of information when analyzing common natural systems. Intelligent systems are usually "sparse" in some domain. That domain unfortunately is a transform away from its natural state. However, upon transformation, this means that one can get a perfectly accurate sample of data with one-tenth the sampling rate for example. The trick is to find the domain in which it's sparse and transform the signal before or during the measurement!

Publications:

Wavelet Transforms

For years Short-Time Fast-Fourier Transforms were the only way we analyzed the spectrum of signals in real-time.

H-Bridge

To take advantage of a small voltage and control larger voltages both negative and positive one uses the H-bridge

EE Principles used in Project 8

Here are some of the presentations that were made while working at Penn State:

T. Wendler Final Report (semi-Technical)

During my postdoc appointment at Penn State I was tasked with developing the Phase III detector for Project 8. A major change from previous phases of the experiment was that we moved into the far-field of the CRES source to cover a larger volume. Having no structures near the source means we have to rely purely on the radiative power transfer and can not exploit any reactive “modal” coupling (i.e. TE01 in a waveguide) as in the previous phases. A wide variety of antenna topics have been covered while studying the large volume demonstrator. This folder contains most of my presentations while at Penn State. A few helpful references for antennas and array design are here. Below is a list the general research developments in this effort followed by an synopsis of each: CRES Synthesis Power Combining Transmit vs. Receive mode Far/Near-field properties Maximum Power Transfer Theorem From Frequency to Time-domain with Impulse Response (HFSS to Locust)

Power Combining

After the incident field on an antenna has been converted to a travelling-wave voltage signal on a transmission line, the voltage wave propagates to the amplifier. Since the PIII design involves passive arrays of antennas, it is often the case that multiple antennas are coupled to one amplifier through a feed network. The purpose of power combining in Locust is to sum and propagate these signals accurately through the network to the amplifier. The signal propagation is done semi-analytically in Locust: the amplitude of the signal is derived either from HFSS or an equivalent circuit model, and the phase is calculated analytically assuming mod(2pi) electrical spacing between elements. Some of the details are described in presentations here including “power combining” (or dividing) in the title such as this patch array study and this slot array study. Many of the Locust results are shown alongside analogous computations in HFSS by Arina T. and Penny S. presentations on Basecamp. This Locust/HFSS interface has served as a general cross-check for the coding of the power combiner, although simple analytic impedance calculations have been used as well. One fundamental discovery made by the antenna team was that the ideal junction S matrix in a passively combined linear array would need to include a high directivity for the LNA-side output, a single port of a 3 port junction. The following S-matrix represents the ideal junction for a phased array with maximal axial coverage and ideal power combining losses through evading reradiation: S=[1,1,1:0,0,0:0,0,0]. In this matrix one can see that port 1 output is highly favored over the others. Unfortunately, EM laws prevent us from creating a simultaneously matched, reciprocal, and lossless network (Pozar p.318). Circulators and Isolators are devices that come close as they use ferrous materials to enforce non-reciprocal behavior. The Wilkinson divider also has a similar property to that which we are looking for, isolation between two ports. Moreover, the junction efficiencies highly depend on what mode they are in, even-mode (100%) or odd (0%) or something in between (asymmetric amplitude and/or phase between the inputs). For example, in the Wilkinson divider odd-mode produces total destructive interference while even-mode produces the complete opposite. Perhaps the most important feature we had to address in power combining was the possibility of the incident signals on each junction not only being unequal in phase but also amplitude. This was mostly a near-field effect. We do indeed anticipate this near-field phenomena where the signal’s incident on each of the junctions are not only asymmetric in phase but also in amplitude in the FSCD. A last but most important part is that these are specifically called Power Dividers and NOT Voltage Dividers, therefore, the outputs are NOT simply a superposition of voltages of the inputs! One way to reconcile this with the irrefutable idea of EM being a linear theory is by considering the transformation of impedances of the junction in question.