9.2. Current Source with Source Degeneration
It is normally desirable to have the output resistance of a current source as large as possible. It can be improved over the circuit of Fig. 9.1 by adding resistance in the source branch, as shown in Fig. 9.2, to establish source degeneration (negative feedback). In the discussion of the signal circuit, it is necessary to represent the diode-connected transistor with its linear equivalent, which is just a resistance of magnitude, 1/gm. This can be seen by inspection of the circuit of Fig. 9.3. The voltage, Vd, is applied directly to the gate such that Vgs = Vd and the drain current is Id = gmVd. Thus the resistance of the diode is just Vd/Id = 1/gm. The result is the same for the PMOS and NMOS as is always true for signal linear models.
Figure 9.2. Current-source circuit with source resistors to improve output resistance at drain of current-source transistor, M2.
Figure 9.3. Signal circuit for diode-connected NMOS.
The new output resistance at the drain of M2 for the current-source circuit with source resistors (Fig. 9.2) can be derived based on the signal circuits shown in Fig. 9.4. The output resistance is defined as Ro = Vo/Io, where Io is the drain current flowing in conjunction with the application of the test voltage Vo. Figure 9.4(b) replaces M3 with the signal model equivalent and M2 with the ideal, intrinsic transistor model (current source) along with output resistance,1/gds2. The transistor symbol represents the ideal transistor with output current gm2Vsg2, positive in the direction shown.
Figure 9.4. (a) Signal circuit of Fig. 9.2. (b) Reference transistor circuit replaced with the linear model. The effective resistance at the gate of the current source transistor plays no role other than to return the gate to ground since Ig2 = 0.
The current Io flowing through the transistor and up through the resistor, RS2, develops a voltage across the resistor, VRS2 = IoRS2. Since Ig2 = 0, an input circuit loop equation is simply Vgs2 = –IdRS2. The transistor linear-model current source, gm2Vgs2, thus is down, as shown in the signal-circuit diagram of Fig. 9.4(b). The sum of currents through 1/gds is
Equation 9.6
The voltage Vo is thus
Equation 9.7
and the output resistance is
Equation 9.8
This magnitude can be assessed with the use of (4.5), which is gm = 2ID/ Veffp. Eliminating gm in (9.8) results in
Equation 9.9
If the magnitude of the voltage across RS2 is several volts, then Ro is much greater than 1/gds2, since Veff2 is typically a fraction of a volt. In integrated circuits, RS may be replaced with an additional current source, in which case the expression becomes
Equation 9.10
where the output resistance of the added current source is approximately 1/ID2λp [(4.13)].