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Since an analytical expression for the drain current is known (equation 1026), we can actually determine gm as given by gm = [k(vGS VT )2 ] vGS (1033)

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at the operating point (IDQ , VCSQ ) Thus, evaluating the expression for the transconductance parameter, we obtain the expression

(1034)

where gm is a function of the quiescent drain current, as expected, since the tangent to the iD -vGS curve of Figure 1025 has a slope that is dependent on the value of IDQ The next two examples illustrate the calculation and signi cance of the transconductor parameter in MOSFETs

Schematics, Diagrams, Circuits, and Given Data: VDSQ = 35 V; VGSQ = 24 V; Assumptions: Use the MOSFET model of equation 1029 Analysis: First, we compute the quiescent drain current:

gate-source voltage, the drain current will increase by 035 mA The MOSFET clearly acts as a voltage-controlled current source

term Object to indicate an in-memory instance of a class s code. You will find more on this meaning of the term Object later in the More on Objects section of this appendix.

Determine the gate and drain-source voltage and the drain current for the MOSFET ampli er of Figure 1026

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Schematics, Diagrams, Circuits, and Given Data: R1 = R2 = 1 M ; RD = 6 k ;

Assumptions: The MOSFET is operating in the saturation region All currents are expressed in mA and all resistors in k Analysis: The gate voltage is computed by applying the voltage divider rule between Figure 1026

resistors R1 and R2 (remember that no current ows into the transistor): vG = R2 1 VDD = VDD = 5 V R1 + R 2 2

10

As you can see, Microsoft has created many built-in types for your convenience. Having a set of predefined types makes programs, even when written by many different people, more consistent. This, in turn, makes it easier for one programmer to see someone else s code and know how a type of data was intended to be used.

Assuming saturation region operation, we write: vGS = vG vS = vG RS iD = 5 6iD The drain current can be computed from equation 1029: iD = k (vGS VT )2 = 05 (5 6iD 1)2 leading to

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with solutions: iD = 089 mA and iD = 05 mA To determine which of the two solutions should be chosen, we compute the gate-source voltage for each For iD = 089 mA, vGS = 5 6iD = 034 V For iD = 05 mA, vGS = 5 6iD = 2 V Since vGS must be greater than VT for the MOSFET to be in the saturation region, we select the solution: iD = 05 mA vGS = 2 V

The corresponding drain voltage is therefore found to be: vD = vDD RD iD = 10 6iD = 7 V And therefore vDS = vD vS = 7 3 = 4 V

that the condition for operation in the saturation region is indeed satis ed: vDS > vGS VT leads to 4 > 2 1; since the inequality is satis ed, the MOSFET is indeed operating in the saturation region

In .NET, types are divided into two categories: reference types and value types. These names identify how .NET stores and refers to the data through the variables and constants. To help you understand the difference, consider the kind of things a computer must track to allow you to use a variable or constant. The computer would need the name, data type, and address in memory where the actual values are stored. It may be useful to think of what the computer stores as a table of values, as shown in Table B-5.

The transconductance parameter allows us to de ne a very simple model for the MOSFET during small-signal operation: we replace the input circuit (gate) by an open circuit, since no current can ow into the insulated gate, and model the drain-to-source circuit by a controlled current source, gm VGS This small-signal model is depicted in Figure 1027

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