# Current voltage relationship in mosfet circuit

### The Basic MOSFET Constant-Current Source

In your circuit, R1 limits your drain current to about 1 milliamp, which is pretty small. It looks like it only takes a Vgs about half a volt above Vt to. Inversion layer under gate (depending on gate voltage). • Heavily body voltage important. Key elements: ;;;;;;;;;; Circuit symbols Want to understand the relationship between the drain current in the MOSFET as a function of gate-to- source. In most MOSFET applications, an input signal is the gate voltage V. G and the . With the gate voltage above the threshold, the drain current, I d., is given by. Id .. To simulate MOSFETs in electronic circuits, we need to have models for both.

Transistors functioning as linear amplifiers need to be biased such that they are operating in a desirable portion of their transfer characteristic. This predetermined current needs to be stable and independent of the voltage across the current-source component. Of course, no real circuit will ever be perfectly stable or perfectly immune to changes in voltage, but as is usually the case in engineering, perfection is not quite necessary.

Also, IC manufacturing technology favors transistors over resistors. As you can see, the drain of Q1 is shorted to its gate. So, is Q1 in cutoff, the triode region, or the saturation region? We can customize this reference current by choosing an appropriate value for RSET.

## The Basic MOSFET Constant-Current Source

So what does all this have to do with Q2? Well, the drain current of a MOSFET in saturation is influenced by the width-to-length ratio of the channel and the gate-to-source voltage: Now notice that both FETs have their sources tied to ground and that their gates are shorted together—in other words, both have the same gate-to-source voltage.

Thus, if we assume that both devices have the same channel dimensions, their drain currents will be equal, regardless of the voltage at the drain of Q2. This voltage is labeled VCS, meaning the voltage across the current-source component; this helps to remind us that Q2, like any well-behaved current source, generates a bias current that is not affected by the voltage across its terminals.

### MOSFET analysis

Another way to say this is that Q2 has infinite output resistance: Under these conditions, no current ever flows through the output resistance RO, even when VCS is very high. This means that the bias current is always exactly equal to the reference current. And the name is particularly appropriate when you consider the visual symmetry exhibited by the typical schematic representation.

The linear model as described by equation 7. Both sides of the equation can be integrated from the source to the drain, so that y varies from 0 to the gate length, L, and the channel voltage VC varies from 0 to the drain-source voltage, VDS. According to the above equation the current would even decrease and eventually become negative.

The charge density at the drain end of the channel is zero at that maximum and changes sign as the drain current decreases. As explained in section 6. However, these holes cannot contribute to the drain current since the reversed-biased p-n diode between the drain and the substrate blocks any flow of holes into the drain.

Instead the current reaches its maximum value and maintains that value for higher drain-to-source voltages.

A depletion layer located at the drain end of the gate accommodates the additional drain-to-source voltage. This behavior is referred to as drain current saturation.

Drain current saturation therefore occurs when the drain-to-source voltage equals the gate-to-source voltage minus the threshold voltage.

## Chapter 7: MOS Field-Effect-Transistors

The value of the saturated drain current, ID,sat. An example is shown in Figure 7.

The dotted line separates the quadratic region of operation on the left from the saturation region on the right. The drain current is still zero if the gate voltage is less than the threshold voltage. However, it is possible to forward bias the drain-bulk p-n junction. A complete circuit model should therefore also include the p-n diodes between the source, the drain and the substrate.

### Relationship between Vds and Vgs- MOSFET - Electrical Engineering Stack Exchange

We now use the quadratic model used to calculate some of the small signal parameters, namely the transconductance, gm and the output conductance, gd.

The transconductance quantifies the drain current variation with a gate-source voltage variation while keeping the drain-source voltage constant, or: In saturation, the transconductance is constant and equals: Therefore the drain current equals: The measured drain current in saturation is not constant as predicted by the quadratic model.

Instead it increases with drain-source voltage due to channel length modulation, drain induced barrier lowering or two-dimensional field distributions, as discussed in section 7. A simple empirical model, which considers these effects, is given by: The variable depletion layer model Next, we develop the variable depletion layer model, which includes the variation of the charge in the depletion layer between the source and drain.

This variation is caused by the voltage variation along the channel. The inversion layer charge is still given by: We can now apply the linear model to a small section at a distance y from the source and with a thickness dy.