Circuits and YOU!

One of the most valuable elements in modern electronics is the transistor. The transistor has allowed electronics to go from a hobby to an industry. The transistor allows your circuit to work with large signals, small signals and interface between the two. Transistors are at the base of amplifiers, digital systems and practically all sensors.

The biggest thing with transistors is that they no longer follow ohm's law. We will now start working with elements that follow relationships not governed by simply V=IR. The relationships between our voltages and currents will be determined by transistor configuration. KVL and KCL will still hold, but where going to have to be careful when we use them.

The Theory
Transistors are made possible by semiconductors. A semiconductor is a material that can be in a conducting state, or an insulating state based upon the voltage applied to it and its intrinsic properties.

Charged Silicon
Silicon by itself, is neither a good conductor or insulator. Its just a pretty decent resistor. One of the things we can do is to "dope" silicon. doping is when we add impurities to the silicon to change its conductive properties a little bit. What gives silicon it's conductive properties is the fact that silicon likes to bond to itself and form a crystal lattice. In this lattice, the silicon's valance electrons are all shared with neighboring silicon atoms. Since all the spare electrons are help up in this bond, any extra electrons (your electric current) have a hard time jumping from silicon to silicon. However, the energy needed to bump an electron out of its orbit, isn't that much, so there still is a flow of current through regular silicon, it just isn't that much.

When we dope silicon we take atoms which have one extra valance electrons, or one fewer electrons. What this does is either gives us a material with an overall positive charge (P type silicon) with excess holes (positive charged nucleus) or overall negative charge with excess electrons (N type silicon) This excess of movable charge allows current to flow. So p type and n type silicon are themselves decent conductors. How conductive a piece of p-type or n-type silicon is, is determined by carrier concentration and charge mobility (along with other factors). We can choose carrier concentration by how much we dope the silicon and mobility is determined by the majority charge carrier (electrons for n-type and holes for p-type). Naturally, electrons are more mobile so n type is usually more conductive than p type with similar doping. This is all fine and dandy, and is great science for making really good resistors, but to make a silicon device we have to look at the barrier between a piece of p-type silicon and n-type silicon.

Band Theory for dummies
I am not going to go in depth into band theory, but I will go over as much as you need to know to have an understanding of our devices. We know that like charges repel and opposite charges attract. Charges in our silicon are mobile and can move around. When we put a piece of nSilicon and a piece of pSilicon we form what is called a depletion region. The holes combine with the electrons and we get neutral charged silicon. This forms a barrier between between the pSilicon and nSilicon and charge no longer flows. Because we have a separation of charge, we have a built in potential and this is the key to silicon devices.

PN junction diode
The simplest device we can have is just a PN junction and with that junction we form a diode. A diode is a device that allows current to flow in one direction.

We discussed how a PN junction has a natural build in electric field caused by the separation of electric charge due to the creation of a depletion region. If we are to sketch this as voltage across the diode we get something like:

When we apply a voltage to out diode, that voltage will affect our built in potential. If it is the same polarity as the built in potential, our diode's potential hill increases and doesn't allow current to flow:

However, when we apply a voltage, opposite polarity of our built in potential, we create a potential hill that allows our current to flow. However we lose the built in potential to our diode and the voltage across our circuit is the voltage of our source minus the built in potential voltage:

Thus, a diode allows current to flow only in one direction, the one which opposes the built in potential and creates a potential hill that our electrons may pass through.

So here we see how a PN junction in silicon creates a useful device. This is the basis for all silicon devices. By taking advantage of the geometries and modifying the band structure of a crystal we can build silicon devices to do almost anything.

The transistor.
A transistor is another type of silicon device. For all intensive purposes there are two transistors that we are concerning ourselves with, the Bi-polar Junction Transistor (BJT) and the Metal-Oxide-Semiconductor transistor. Both transistors have the same general principles (they can both act as switches and both are amplifiers) however, they operate on vastly different mechanics and each have their own advantages.

The BJT
A BJT is made with three layers of semiconductors either NPN or PNP. The arrangement determines it's polarity. For the purpose of the rest of this document, we will be working with NPN transistors, for PNP everything is the same except we invert the biasing. (i.e. we now need -.7v to “turn on” the transistor). BJTs were the first practical transistors (however not the first theorized) BJTs have great transconductance (the ability to control output current with input voltage) and have some nice features which make them very practical to model. However, BJTs are trickier in the fact they have finite input and output resistances which must be take account for. All BJTs have three terminals, the base collector and emitter.

Principle of operation
The way a BJT works is that a signal on the base of the transistor allows a larger current to flow from the collector to the emitter.

A transistor is a device that is not linear, and it doesn't follow one equation the way, say a resistor does.

Depending on several variables (Base Current, Collector-Emitter Voltage) we get different Collector currents.

Now, there are three modes of operation worth looking at:

-Cutoff: This mode is where there is no base current present and the transistor is off, no current flows from collector to emitter

-Saturation: This mode is where the transistor is fully conducting, this is the same as a logical 1.

Switching VS Amplification
The most used aspect of a transistor is its ability to be an electronic switch. The philosophy behind this is that we can use a small signal from say a microprocessor to control large electric objects like DC motors (For more on this check out mcuplace.com). However, for this blog we will be looking at transistors as amplifiers and because of that, the most useful region of operation is the forward active mode.

Forward Active
Typically to be in the forward active mode both the base-emitter diode is forward active (>.7v) as well as the base-collector diode. We also have the constraint of collector-emitter voltage >.3V. As long as we satisfy those three conditions we are in forward active region. When the transistor is in this mode, it behaves by the following formula

Where Beta is a parameter of the transistor.

Transistors are complicated devices in that there's no simple way to figure out whats going to happen with a circuit. When designing a circuit, we generally have goals we'd like to accomplish and we use the following above as assumptions to find the collector current. Once we know the collector current, we can see how variations in base current (voltage) produce variations in collector current (voltage) allowing us to amplify signals. Before we can do that, we have to model the transistor in a static DC case and figure out some parameters.

Q-Point and biasing
Biasing is the act of choosing our DC base current so that we can get proper signal amplification. We can bias our transistor in many ways. The result however is to find our Q-point base current giving us our Q-point collector current and allowing us to calculate parameters for signal analysis.

So lets start with a circuit:

In this circuit, we have a voltage divider hooked up to the base, and we have a collector resistor and an emitter resistor. The voltage divider allows us to set the base voltage, which determines our base current, and our collector current.

Quick Dirty Analysis

Analyzing a circuit like this can be a nightmare, if we take out time and stick to what we know, we can analyze every aspect of this circuit and find the exact currents and voltages... OR we can make a bunch of assumptions and get a good enough approximation.

First thing we know, our VCC is 5V, with our voltage divider we get a VB of 2.5V. Since the voltage drop across VBE is .7V we know VE is 1.8V. The current that goes through RE is the same (approximately) as RC so 1.8/1k is 1.8ma. Thus Ic is 1.8ma. Now we know our collector current we can go on to do signal analysis.

Checking our approximation

The easiest thing we can do, is use PSPICE to verify our circuit.

As you see, our guestimations are pretty close to what Pspice decided to spit out. So lets start analyzing what happens when we put a signal on our circuit.

Signal Analysis

For signals, we use a different type of model, one that allows us to not worry about recalculating every parameter of our circuit at every instance of our changing signal. For this type of model, we simply find the q point characteristics and shove it into our model. Lets take our circuit and modify it a little bit.

We've added quite a bit to our circuit but all will be explained in a moment. First off, we added an AC source which will be our signal. Like all sources it has a finite output resistance RS. We add CC1 as a Coupling Capacitor, this isolates our AC and DC parts of our circuit so that current from our biasing circuit doesn't flow into the source. This works because fundamentally, capacitors act as a DC block, they only allow AC to flow. Next, we add CE, this capacitor will increase our gain of the circuit and will be more apparent once we build our model. Finally we add a load resistor and another coupling capacitor, again we want to separate the AC and DC portions of our circuit.

Hybrid-Pi Model

What our model does, is take our complicated transistor and reduce it to a few resistors and a current source like such:

(photo courtesy of wikipedia)

This model allows us to replace the transistor in our circuit with the model above (note the Base Collector and Emitter nodes)

To build our model with have to define a few parameters:

: This is our imput resistance defined as where Vt is the thermal voltage and Ib is base current

Ro: Output Resistance, this is defined as where Va is the Early voltage(intrinsic parameter) and Ic is the collector current.

Gm: Transconductance, is defined as

Thermal Voltage is a relationship derived from Boltzmann's constant that correlates to the intrinsic voltage in a semiconductor junction. It is dependent on temperature, but for most cases it is 26mv.

Early Voltage is a theoretical voltage, that relates to our output resistance. For the transistor in the circuit the 2n2222 the early voltage is around 100v (you can look this up in the data sheet hopefully)

Ib, the base current should be . is approximately 150, but we can just use our PSICE values.

Ic, was shown to be approx 1.8ma.

With those parameters we find:

gm ~ .07 a/v

So lets construct our signal circuit with the above parameters. Now, we are building a circuit for signals and thus there are a few things to be aware of:

With respect to a signal in circuits, power and ground are the same thing, thus in our above circuit with the voltage divider, those resistors are actually in parallel with respect to a signal, thus we can convert them to a common resistor to ground.

Capacitors are a low impedance connection with respect to AC, thus they are shorts to our signals. The purpose of CE becomes a little more clear, rather than connecting to ground through RE, we can connect R pi directly to ground increasing the voltage drop across it and the signal gain.

With those considerations our circuit becomes:

First thing we want to calculate is our voltage gain AV

For our circuit Av = -35.

Thus any input signal should be amplified -35 times. Note the input voltage is after the signal source, with our current circuit the output resistance of the source dwarfs the input resistance of the amplifier, thus we have a large voltage drop across the source resistance and very little across our amplifier... oops...

Three types of amplifiers.

The amplifier we just analyzed is called a common emitter amplifier. We call it this since the emitter shares a connection to the input and output (namely the ground) There are two other types of amplifiers, Common Base and Common Collector. All can be analyzed using similarity techniques and all have different properties.

Common Emitter: Large voltage gain but worst bandwidth

Common Collector: Large current gain, Large input impedance, low output impedance, unity voltage gain.
Common Gate: Best frequency response, low input impedance, unity current gain, low voltage gain.

Now, each amplifier excels at one task, but they are most useful when combined together. The idea behind cascade amplifiers is to use buffers and these amplifier configurations to maximize performance and gain while no suffering the drawbacks of any one design.

MOS transistors
Metal-Oxide-Semiconductor Transistors are very similar to BJTs in the fact they act as both amplifiers and switches. Even the design methodologies are very similar. However the design principles are completely different. MOS transistors, like BJTs have three leads. Gate (base) Drain(Collector) and Source(emitter). However the similarities stop there. Due to the sheer size of this article, I will hold off on talking to much about MOS transistors.

I hope this article served as a nice guide into doing design work with transistors, I've barely scratched the surface when it comes to using these devices. Note we've only covered one mode of operation and barely at that. There is much more to learn about these devices but unfortunately, I don't have the time or knowledge to do so at this time. I look forward to posting much more on this topic as well as exploring more theoretical topics and possibly even device fabrication.