Common Emitter Amplifier

cea1

The common emitter amplifier accepts AC signal inputs and amplifies the entire AC input signal. For this circuit to work however, the common emitter amplifier requires biasing to operate between the minimum and maximum peak values on the input signal. It is also necessary to keep the transistor operating in active mode.

In amplifier design, minimizing distortion is a major issue. The Q-point or quiescent operating point of an amplifier is the DC operating current or voltage at the transistor with no input signal supplied. The Q-point for a transistor is typically half of the supply.

 

Voltage Divider Biasing

To achieve correct biasing, R1 and R2 must be chosen to maintain the base voltage at the transistor at a constant level. The base voltage VB is a function of the supply voltage and the two resistors at the base of the transistor.

cea2

Once the amplifier is properly biased, the voltage gain calculation is shown below. An important note is that the gain of the circuit is different for low frequencies than it is for high frequencies and the gain is then a function of the load resistance and the internal resistance of the transistor. Coupling capacitors C1 and C2 are used to separate the AC input signal from the DC biasing voltage.

cea3

Wave Optics – Transmission, Grating and Lenses

Through a transparent plate with no angle of incidence, a plane wave continues to propagate through the plate, but with an altered wavenumber n*k0, where n is the refractive index and k0 is the wavenumber of the plane wave before transmission through the plate.

transplate

Where d is the thickness of the plate and U(x,y,z) is the complex amplitude of the wave, the transmittance of a plane wave in a homogenous, transparent plate is described as:
t(x,y) = U(x,y,d)/U(x,y,0) = exp(-j*n*k0*d).

Given the scenario of a plane wave with wavevector k and angle of incidence θ, the formula is altered and may be modeled using Snell’s Law:

sinθ = n*sinθ,

exp(-j*k1 • r) = exp[-jnk0(zcosθ1 + xsinθ1),

t(x,y) = exp(-j*n*k0*d*cosθ1).

tras

A prism may be used in the following manner to direct the propagation of a plane wave:

prism3

Further, a thin lens may be used to focus a plane wave, converting it into a paraboloidal wave.

thinlens

A graded-index (GRIN) lens may be used to produce the same effect:

grin1

Diffraction Grating is a method of modulating either the phase or amplitude of an incident wave. An incident plane wave is split into multiple plane waves. They may also be used as filters or spectrum analyzers.

grating1

The grating equation is as follows:
θq = θi + q*λ/Λ,
where θq is the angle of resultant wave(s),  θi is the angle of incidence, q is the diffraction order (0,1,2…) and Λ is the period of thickness variation in the diffraction grating. Since the device is dependent on the wavelength, it may be used to produce a polychromatic wave, separating it’s spectral components in the following manner:

grating2

(1) B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Hoboken: Wiley, 2019.

Diode Voltage Clipping Circuits

We’re already discussed the PN junction in a previous post. Let’s explore some of the applications of the PN diode.

diode2

It was already discussed that due to the nature of the PN junction, current is only allowed to flow in one direction. This results in two possible scenarios using a diode, depending on the direction it is facing with respect to the source.

diode1

Diode Clipping Circuits

Diodes in a forward bias allow current to pass, but thereby reducing the voltage level. In a reverse bias, current is stopped but the voltage remains unaffected.

Diode clipping can be done for either the positive or the negative voltage of a sinusoidal (or analog) input voltage. In order to clip both the positive and negative sides of the input voltage, two diodes are needed.

Positive voltage clipping:

d1

Negative voltage clipping:

d2

Two Diodes:

d3

If 0.7 Volts is not the desired output clipping voltage, a bias voltage can be added in each situation above.

d4d5

Wave Optics – Reflection, Refraction

Reflection of Optical Waves on a mirror may be modeled using the Helmholtz equation, k1 • r = k2 • r, where r = (x,y,0) (following the example below on the z = 0 plane), k1 = (k0*sinθ1, k0*cosθ1) and k2 = (k0*sinθ2, k0*cosθ2). The wavenumbers k1 and k2 in this formula, is assumed to be equal as this is one property of reflected waves. This simplifies to the expression θ1 = θ2, which means that the angle of incidence is equal to the angle of reflection.

mirror2

 

Refraction of Optical Waves at a planar boundary can be described using the Helmholtz equation and Snell’s Law. For the below scenario, where k1 is the incident wave, k2 is the refracted wave and k3 is the reflected wave, the Helmholtz equation is satisfied by the following vectors:

Helmholtz equation: k1 • r = k2 • r = k3 • r ,  for r = (x,y,0)

k1 = (n1*k0*sinθ1, 0, n1*k0*cosθ1)
k2 = (n2*k0*sinθ2, 0, n2*k0*cosθ2)
k3 = (n1*k0*sinθ3, 0, -n1*k0*cosθ3)

This relationship may be simplified to show that θ1 = θ3 (essentially proven in the previous example of reflected waves) and n1*sinθ1 = n2*sinθ2 (Snell’s Law). Note that it is not possible with Wave Optics to describe the magnitudes of the incident, reflrected and refracted waves and a more rigorous method, such as Electromagnetic Optics is required to explain such phenomenon.

refract1

 

(1)  B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Hoboken: Wiley, 2019.

Messing with Substrates (10 GHz bandpass filter) [silly]

In this post we will take a reasonable 10 GHz bandpass filter (at least for a new grad student) and see how a new substrate will change how this filter works.

This is the original bandpass filter with the standard substrate:

messybp2

messybp1

If you can read the numbers on the above pic, you could also build this filter. Let’s get a better picture of what the substrate is for the original circuit:

messybp3

 


Let’s try a silicon dielectric, shall we?

messybpsilicon

One thing is for sure – it’s not a bandpass filter anymore.messybpsilicon2

 


Let’s add a 20 mil Indium conductive layer below the dielectric:

messybpindium

Voilà! It’s centered at 8 GHz! Brilliant!

messybpindium2

 


Here’s a thought – how well does your bandpass filter work underwater?

messybpwater1

It looks like your bandpass filter might give you a little gain there at some frequencies in water!messybpwater2

 

Microstrip Lange Coupler (5 GHz)

The Lange Microstrip (quadrature) coupler is known for it’s low loss, wide bandwidth and compact layout. Similar to other couplers, it consists of an isolated port, through port and coupled port.

You can build a microstrip Lange coupler using the DesignGuide tool in ADS:

langec0

 

These are the results for the equation-based simulation. These results admittedly look considerably better.

langecoupler2

 

This is the substrate used:

langecoupler1

 

These are the results for the momentum simulation. Admittedly, some tuning would improve this considerable.

langec3

And here is the layout component:

langec4

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.

antennapattern.jpg

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.

directibity.jpg

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.

The Oscillator

The oscillator is an important concept used in a variety of applications. One basic use of an oscillator is that of signal generation.

An oscillator is a system with a gain and positive feedback. The gain must be greater than the loss in the feedback system, so that each time the signal goes through the aplifier in the system, a net gain is produced. The phase shift of a single round trip in the gain-feedback loop must also be a multiple of 2*pi so that a pure signal is repeatedly amplified.

When these conditions are satisfied, the system is unstable and oscillation begins. Eventually, the amplifier gain becomes saturated and rather than a further increase of amplification, the added gain only compensates for system losses.oscillator

Since the system is dependen upon a 2*pi phase shift (the period), an oscillator may be designed for a specific frequency. An oscillator generate a signal from noise by repeatedly amplifying the noise periodically.

Although there are many applications for oscillators, a laser is fundamentally an optical oscillator, an optical signal generator. The maser, which stands for microwave amplification by stiumulated emission of radiation was used before the laser. The saser is an acoustic version of the laser, in which instead of emitting a beam of photons or electromagnetic radiation, an acoustic beam or signal is generated.

The following outlines the operation of a laser; an optical amplifier placed inside of a resonator with a partially transmitting mirror as the output of the system.

laser2

B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Hoboken: Wiley, 2019.

 

ECE530 Advanced Electronics and Optoelectronics 1/21/2020 Class Notes (1st lecture)

 

Textbook:        High speed electronics and optoelectronics: devices and circuits, by Sheila Prasad, Hemann Schumacher, and Anand Gopinath, Cambridge university press, 2009

Learning objective:    Principles of advanced electronics and optoelectronics are illustrated by showing their applications in advanced radar, wired/wireless communications, and electronic sensing. Key electronics/photonics devices including high speed transistors, diodes, lasers, high frequency modulators, photodetectors, amplifiers and passive circuitries are discussed.

Outcome:       Following the completion of this course students will be able to

  1. Perform quantitative analysis of electronic and photonic systems using the basic principles covered in this course that include: wave propagation through dielectric media and optical waveguides, high frequency electronic circuits, generation and detection of light from semiconductor devices including semiconductor lasers, light emitting diodes and photodetectors and the modulation of light through the electro-optic
  2. Articulate state-of-the-art electronics and photonics technology and future trends
  3. Apply the theory of operation of electronic and photonic devices
  4. Articulate the performance and design trade-offs amongst RF, Digital, and Photonic solutions in EW architecture

COURSE OUTLINE

  • Review of semiconductor materials and physics
    1. Semiconductor materials/crystal structure (1 week)
    2. Carrier transport/recombination/generation (2 week)
    3. Heterostructures (1 week)
  • Electronic devices
    1. High speed FET (2 week)
    2. High speed HBT (1 week)
  • Optoelectronics
    1. Optical sources (2 week)
    2. Photodetector (2 week)

 

 

Review of Quantum Mechanics

A course in devices would not be complete without device physics. The foundations of semiconductor devices are… Quantum Mechanics! A good resource for review in Quantum Mechanics, aside from the course textbook is the Quantum Physics course provided by MIT OpenCourseWare. This includes video lecutres, assignments, exams and more for three whole semesters’ worth of Quantum Mechanics. Quantum Physics is also important for studying the subject of Photonics and Quantum Electronics deeper and is necessary to become an expert in a related field. More review of Quantum Mechanics is to come soon.

Quantum Physics I
Video lectures: https://archive.org/details/MIT8.04S16/
Syllabus: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/syllabus/

Quantum Physics II
https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/

Quantum Physics III
https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii-spring-2016/

Other courses available are found here: https://ocw.mit.edu/courses/find-by-topic/

 

T-CAD, RSoft

This course features the use of Rsoft and T-CAD, Silvaco for device modeling, doping and bandgap engineering problems.

 

Semiconductors

Silicon wafers (~4″) go for about $20. GaN wafers on the other hand go for about ~$1k. The price differential may be one of the few things silicon has going for it. In other cases, consider that Silicon does not work at high speeds. For high speed semiconductor devices, III-V semiconductors are preferred and will work better. One other interesting downside of Silicon is that it is unable to emit light.

5301

The Hybrid HBT is a better option for transistor technologies at higher frequencies. The HBT features higher electron mobility.

5302

This course will also feature study of Ternary and Quarternary Compounds. Quarternary compounds are used for quantum well lasers. Ternary Compounds feature one variable x where quarternary compounds feature two variables x,y. Another important ternary compound not listed in InGaAs.

 

Material Growth

We will also discuss the process for fabrication and material growth. Material growth and fabrication is a process that generally requires a high level of technological know-how and thus only few countries manage to perform this operation. Currently, it is even possible to grow one atomic layer (Angstrom) at a time. Two methods of material growth are MOCVD (Nobel Prize awarded for this discovery) and MBE (should also get a Nobel Prize soon). MOCVD is particularly best for producing many at the same time, while MBE is better used for research production.

 

Bell Laboratories

As an aside, consider the company that had existed before breaking up, Bell Laboratories. At Bell Laboratories, given a monopoly it was able to fund scientists and researchers to conduct free-range scientific research and discovery. Today, researchers at Universities (primarily) need to provide evidence of advancement ever 6 months or so. A program such as Bell Laboratories allowed for aimless research to be conducted, which ended up being far more successful than could have been imagined.

 

Types of Solids

Consider the three types of solids, Crystalline, Polycrystalline and Amorphous. Crystalline structures feature atoms that are aligned periodically and produce a unique shape (example: Quartz). Polycrystalline solids include ceramic, saphire, even possibly other metals such as steel. Interesting point about saphire – saphire is used in PCVD as a film. Amorphous solids include liquidated solids, glass and other liquids.

5303

Semiconductors feature a lattice structure as the two below:

5304

 

Crystal Directions and Planes

The following are three types of crystal directions and planes:

5305

It is of note that etching in crystals must be done in only certain directions according to the ‘grain’ of the crystal. In order to split a waver along a grain, make a notch at one point on the side and apply a pressure to the wafer.

 

Atomic Bonding
It is important to review the effect of covalent bonding between valence electrons.

5307

Next class, the topic of wave equations will be covered.

 

 

Review of OP-AMPs

Operational Amplifiers perform a number of different tasks such as amplification, filtering and performing mathematical operations. This is a review of a number of concepts related to OP-AMPS.

Open Loop and Closed Loop Gain

An op-amp’s amplification (open loop gain) without any feedback in the system is usually very large (~100,000 x). The system without any feedback is referred to as an open loop system. A closed loop system provides feedback to the system.

Capture1

The feedback in a system is determined by the impedances of the feedback loop and the input of the system. Furthermore, the op-amp can function as a non-inverting op-amp or an inverting op-amp, producing a system of positive or negative feedback respectively.

Capture2Capture3

It must be said however that the input and feedback impedances must not be only real-values resistances. The following system may easily make use of a complex impedance, and other RC combinations to produce a filter modeled by the transfer function.

Capture4

 

Mathematical operations using OP-Amps

Below are the following Op-Amps:

  • Summing Amplifier
  • Comparator Amplifier
  • Differentiator
  • Integrator
  • Low-Pass Filter example
  • Subtractor
  • Voltage Follower/Buffer

sumop

compopdiffopintegratorlowpsubopvfol

Wave Optics – Introduction

Wave optics describes light with a second order differential equation known as the wave equation. Using the wave equation, optical phenomena that fall outside of the scope of ray optics can be described, such as interference and diffraction. One limitation of wave optics is in it’s inability to describe polarization effects and other phenomena that require a vector formulation.

The wave equation used in wave optics is as follows:

wavefunction

Optical intensity I(r,t) is proportional to the squared wavefunction and is defined as watts/cm^2. This is also referred to as irradiance.

intensity

A monochromatic wave does not vary in intensity over time:monoc

The time-independent equation is known as the complex amplitude of the wave: monoccomplex

And the above formula is the solution to the Helmholtz equation, another important formula used in wave optics:

helmholtz

wavenumber

Where k is the wavenumber.

 

Plane Waves, Spherical Waves, Paraboloidal Waves are the main wave formations.  A plane wave is seen as a wave that continues infinitely along a continuous plane with a constant intensity. The vector along which the plane exists is known as the wavevector. The spherical wave consists of spheres centered about a single point. It may also originate from the centered point or travel inwardly towards the center. A paraboloidal wave is an approximation to the spherical wave using the Fresnel approximation. A paraboloidal approximation is useful for simplifying the interaction of a spherical wave in calculations for diffraction and other situations. Paraxial Waves are a ideal approximation of the interaction of these waves that simplifies many calculations. The approximation leading to the paraboloidal wave is done by considering the spherical wave at a sufficiently great distance, at which only curvatures in the wave are detected. For points very far from the center of the sphere, waves may be treated as plane waves.

paraboloidal

Paraxial optics is an idealization of the directionality of optical rays that allows for approximated results of a number of optical systems. A wave is a paraxial wave under the condition that the wavefront normals are paraxial rays. Under the paraxial approximation of waves, optical rays are perpendicular to optical waves. wavefronts

 

The paraxial Helmholtz equation is as follows:

paraxhelmholtz

(1)

The Zeigenark Effect, Freeing Cognitive Resources

The Zeigenark Effect was outlined by early-twentieth century psychologist Bluma Zeigenark, who proposed and tested with experimentation that an incomplete task would dominate a certain level of cognitive attention, even when not focusing on said task. Obligations left unresolved, therefore are postulated to prevent one from accomplishing other, unrelated tasks. The remaining cognitive resources used for an incomplete task were termed the Zeigenark effect.

Tasks that are left  incomplete, as you may know are virtually endless and most people tend to never run out of things they know they should be doing or will need to finish.

zeigenark

There is a way, however to ensure that the Zeigenark Effect is reduced, even without completing a task, giving one the ability to ignore the task to focus on other aspects of life. The method would be, as one comes to a close on their allotted time for concentration on said task, quickly produce a plan for how the incomplete task may later be completed, best done in writing. Through this method, one may free up cognitive resources to concentrate on other avenues of life and gain an edge whence returning to said incomplete task. If tasks are relatively uncomplicated but are many, one may decide to simply maintain a list of tasks, such that one need not use cognitive resources to stay on track.