Circuits and YOU!

Another type of transistor.

Bipolar Junction Transistors allow us to construct digital logic and they allow us to construct amplifiers. For simple applications, we can model BJTs fairly well. However, from a manufacturing stand point BJTs are not ideal. The base current is energy we must spend to switch our transistor and if we were to extend this to millions of transistors, we find that this type of technology is unfeasible for integrated circuits as we attempt to pack more transistors into a design. Also, BJTs are typically very complicated to fabricate and yield less usable transistors. These hindrances are the main motivation for the development of a better technology, i.e. the field effect transistor.

For quite a while, the idea of a field effect transistor was known however it wasn’t realized in an actual device until the 1960’s. A field effect transistor is once which uses an electric field (An applied voltage) to control the flow of charge carriers. A MOSFET is a type of field effect transistor which uses a topography consisting of a layer of Metal, followed by Oxide and then the Semiconductor.

Mosfets

So a mosfet is a Field Effect Transistor comprised by topography of Metal, Oxide and Semiconductor. The silicon substrate is composed of P-type silicon (for NMOS) with two N-type “bubbles” which form the drain and source. For small signal mosfets, these two regions are exactly symmetric. Just like with a BJT (and any other silicon device) we have a depletion region where the Si where P and N type share a boundary. This depletion region is where the charge carriers (electrons for N type and holes for P type) combine and form a charge gap.

The gate is an isolated terminal from the body of the silicon. There is no connection between the gate and any body structure, thus no current flows through the gate. The gate acts as a control of the charge carriers in the silicon substrate. When a voltage is applied to the gate (with respect to the source) that electric field created pulls electrons (nmos) into the bulk, extending the region of the N+ silicon. Once this reaches a threshold we form a connection between the drain and source and current can flow. There are two voltages that matter when characterizing mosfets. Vds and Vgs. Vds is the voltage from drain to source and Vgs is the voltage from gate to source. The actual operating characteristics of a mosfet are very complicated, but the simple analogy above holds to demonstrate the main operating principles behind this device. We characterize the Voltage at which the transistor becomes conducting as the threshold voltage(Vth). This parameter varies from transistor to transistor and can be from .4 to up to 3 to 4 volts. When we apply a Vgs greater than Vth we form a narrow channel in which electrons can flow. Now, we can use Vgs to control the width of the channel, but also our Vds determines how the channel operates. When Vds is less than Vgs-Vth we operate in ohmic mode where the characteristics of the channel (and thus Id, the current through the drain) are controlled by both Vgs and Vds. Once we increase Vds to Vgs-Vth we form a channel pinch-off and drain current is no longer dependent on Vds. This is called saturation and where most of our modeling will be done in.

3 Modes of Operation:
Cutoff:

Transistor is tuned off, ideally no current flows between drain to source. However we have weak inversion currents that instigate a small Id. Given by the following equation:

Where:

Vt is out thermal voltage (given by Boltzmann distribution}.Cd is the depletion region capacitance and Cox is the oxide layer capacitance.

Lets assume a Vt of 1v, thermal voltage is 26mV at room temperature and we assume Id0 is 1uA. We also assume a Vgs of .7v is applied. We finally assume Cox >> Cd and thus n = 1. After we make all these assumptions we end up with an Id of about 9.74 * 10^-12. This is mostly insignificant and thus for large signal and even small signal that when Vgs < Vth our transistor is off.

Triode or Ohmic Mode:

In this region the channel is formed but it is a narrow. The characteristics of the channel are determined by both Vgs and Vds and likewise the current that flows through it, Id.

Where is the carrier mobility, W is the channel width and L is the channel Length.

This region is when the mosfet operates as a resistor; changes in Vgs produce linear changes in Id. However there is a dependence on Vds which makes this type of arrangement a little more cumbersome for signal analysis.

Saturation:

In this region we form a channel pinch off between the source and drain. The channel is fully created and Vds no longer has an effect on the drain current.

This is the mode of operation we primarily use for small signals.

BJT vs MOSFETS:

For a BJT we would have a base current which determined the amount of current that flowed from collector to the emitter. For a mosfet, we have a voltage on the gate which determines the current which flows from drain to source. Simply put, as we increase Vgs we have increased Id, and modulating Vgs modulates Id which produces an output signal. Q point and biasing is exactly the same as it is for BJTs and we have very similar parameters. Even our small signal model is very similar.

Hybrid – Pi model:

(Image courtesy of Wikipedia)

For our model we have two parameters. Gm, the transconductance:

And Ro the output resistance:

With this we can replace our mosfet in our circuit for signal analysis. Analysis is pretty much the same for MOSFETS as it is for BJTs, but instead we have no resistor between gate and source.

Mosfet Current Mirror:

A very useful circuit is a mosfet current mirror. With this circuit we can construct current sources and accurately bias our amplifiers. This circuit consists of M1 and M2. M1 has R_ref hooked to its drain for VDD while the other is hooked up to a voltage source. The idea is that the current that the M1 branch draws is the current that M2 draws.
In this circuit we know a few things: Vth = 2V for this transistor, and Un * Cox * W/L = 200 ma/V^2 and we need to find R1 to get use 50ma bias current
Using KVl for the M1 branch we get:

We know:

For this arrangement Vgd = Vds. So if we find Vgs we find Vds. We plug in 50ma of Id

We find roots at 2.7 and 1.2 V. Vgs > Vth so the 1.2v root doesn’t make sense. So Vds = 2.7v. Now, if Vds is 2.7V and VDD = 10V, we have a drop of 7.3V across the resistor so R1 = 7.3/Id = 143 ohm.

With this current mirror, Iref is determined by R1, typically we can make R1 a potentiometer and vary it to get the correct reference current. In saturation Id, is determined by Vgs, and since VgsM1 = VgsM2. IdM1 = IdM2. Thus, the reference current we set for the M1 branch is the current that M2 draws.

Now that we have our current source, let’s build our amplifier!

Common Source amplifier with current source:

Let’s assume we have an amplifier like such:

We’re going to let IdM3= IRef = 5ma and Rd be 1Kohm. The equivalent circuit for M3 is:

To find open voltage gain, Avo:

Current gain is infinite since Iin = 0.

Coupling Capacitors
The coupling capacitors in this circuit serve to separate the AC and the DC parts of our circuit. The DC parts of this circuit are our biasing while the AC parts are the signal itself. The bypass capacitor on the source of M3 servers to place a ground on the source for the signal, this increases the effective Vgs and the overall gain of our circuit.

Mosfets as switches
In the following circuit we have a PIC16F690 microcontroller hooked up to a NMOS mosfet used to control an LED:

If you're not familiar with microcontrollers, don't fret, in this circuit were going to assume the microcontroller only generates 1's or 0's. A 1 will represent a voltage of VDD and 0 will represent a voltage of 0. So with the microcontroller, we can turn on and off the LED by generating digital signals. So there are two case:

Where we put a 1 on the gate:
Vgs = 5V which is greater than the threshold voltage. The transistor is in saturation, and it is fully conducting. In this case the channel is completely created and the effective resistance of the mosfet is very very low (a few mili ohms). Current is free to move through the mosfet.

Where we put a 0 on the gate:
The mosfet is in cutoff mode since Vgs = 0 < Vth. No current flows and the mosfet is an open circuit.

So what is the main difference between the mosfet as an amplifier and the mosfet as a switch? Simple put, as an amplifier, we force the mosfet into a region by having a particular bias current. With the source grounded, a large VGS will completely open the channel and the current the mosfet can handle is much greater than the current bounded by the LED and the current limiting resistor.

PMOS
If we take a NMOS transistor and invert the polarity of the layers(N+ bulk with P type Source and Drain), we get a PMOS transistor. The operating principles are the same except the transistor is turned on when Vgs > -Vth. Lets take the same circuit as above except with a PMOS transistor with the same two cases.

When we have a 1 on the output
With a PMOS the source is connected to VDD. With a 1, Vgs = 0 >-Vth, the transistor is in cutoff and no current flows.

When we have a 0 on the output
With a 0, Vgs = -5v < -Vth and the transistor is saturated an fully on.

By inverting the charge of the silicon, we essentially invert the logic. There are a few things to know about Pmos:
The majority charge carriers in a PMOS transistors are holes, which are larger and slower, thus a PMOS isn't as fast (has higher intrinsic capacitance) and generally push less current. However, they are necessary when this type of logic is needed.

The CMOS inverter and CMOS Logic
Here we are going to delve into digital logic since the CMOS gate is a very important part of digital electronics. CMOS stands for Complementary Mosfet, this is a setup composed of both a NMOS and PMOS transistor to form the logic function of a NOT gate.

Again we take our two cases:

When we have a 1 on the input
The NMOS transistor is conducting and the PMOS is not, we see GND on the output, which is a logical 0.

When we have a 0 on the input
The PMOS is conducting and the NMOS is not, we see VDD on the output, which is a logic 1.

As you see, when we put in a 1 we get a 0, and vice versa.

The important thing about a CMOS gate is the fact a MOSFET has no input current. We can make the same arrangement with BJTs but since there is Ib, we lose energy to keep the gate into a state.

However, the fact a CMOS gate doesn't use power is only an idealization. Our computers use CMOS gates to construct their logic and anyone with a laptop will tell you they get plenty hot. One thing to realize is that mosfets do have finite resistances which lead to power losses however, the biggest thing to realize is the fact that our gate is nothing more than a capacitor. To charge and discharge this capacitor it takes energy. Every time we switch our gate we lose that energy we used to charge the gate capacitor. The faster you switch, the more energy you use up. As you increase clock speed, our electronics get hotter!

More?
What else can we do? The answer is almost anything. Mosfets are the primary component used in integrated circuits. Mosfets replace resistors and capacitors in many circuits and even some analog ICs can be made primarily using mosfets. They are incredibly easy to make and the scale incredibly well. They're the primary reason for modern electronics and they will be for quite a while. In the future we will be discussing circuits involving mosfets and other fun stuff!