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EXAMPLE 6.18 Determine IDQ, VGSQ, and VDS for the p-channel JFET of Fig. 6.56. Figure 6.56 Example 6.18. Solution 20 k ( 20 V) VG 4.55 V 20 k 68 k Applying Kirchhoff’s voltage law gives VG VGS ID R S 0 and VGS VG ID R S Choosing ID 0 mA yields VGS VG 4.55 V as appearing in Fig. 6.57. Choosing VGS 0 V, we obtain VG 4.55 V ID 2.53 mA RS 1.8 k as also appearing in Fig. 6.57. The resulting quiescent point from Fig. 6.57: ID Q 3.4 mA VGSQ 1.4 V ID (mA) 8 7 6 5 4 I D 3.4 mA Q - point Q 2 1 – 5 – 4 –3 – 2 –1 01 234 VGS VP Figure 6.57 Determining the Q-point for the JFET configura- VGS 1.4 V Q tion of Fig. 6.56. 290 Chapter 6 FET Biasing For VDS, Kirchhoff’s voltage law will result in ID R S VDS ID R D VDD 0 and VDS VDD I D (R D R S) 20 V (3.4 mA)(2.7 k 1.8 k ) 20 V 15.3 V 4.7 V 6.12 UNIVERSAL JFET BIAS CURVE Since the dc solution of a FET configuration requires drawing the transfer curve for each analysis, a universal curve was developed that can be used for any level of IDSS and VP. The universal curve for an n-channel JFET or depletion-type MOSFET (for negative values of VGSQ) is provided in Fig. 6.58. Note that the horizontal axis is not that of VGS but of a normalized level defined by VGS /VP, theVP indicating that only the magnitude of VP is to be employed, not its sign. For the vertical axis, the scale is also a normalized level of ID /IDSS. The result is that when ID IDSS, the ratio is 1, and when VGS VP, the ratio VGS /VPis 1. Note also that the scale for ID/IDSS is on the left rather than on the right as encountered for ID in past exer- cises. The additional two scales on the right need an introduction. The vertical scale labeled m can in itself be used to find the solution to fixed-bias configurations. The other scale, labeled M, is employed along with the m scale to find the solution ID VP VG G I DSS m= M= m RS IDSS VP 1.0 5 1.0 0.8 4 0.8 0.6 3 0.6 Normalized curve V 2 of ID = I DSS 1 – GSP V 0.4 2 0.4 0.2 1 0.2 0 –1 – 0.8 – 0.6 – 0.4 – 0.2 0 VGS Figure 6.58 Universal JFET bias VP curve. 6.12 Universal JFET Bias Curve 291 to voltage-divider configurations. The scaling for m and M come from a mathemati- cal development involving the network equations and normalized scaling just intro- duced. The description to follow will not concentrate on why the m scale extends from 0 to 5 at VGS /VP 0.2 and the M scale from 0 to 1 at VGS /VP 0 but rather on how to use the resulting scales to obtain a solution for the configurations. The equations for m and M are the following, with VG as defind by Eq. (6.15). VP m (6.35) IDSSRS VG M m (6.36) VP R2VDD with VG R1 R2 Keep in mind that the beauty of this approach is the elimination of the need to sketch the transfer curve for each analysis, that the superposition of the bias line is a great deal easier, and that the calculations are fewer. The use of the m and M axes is best described by examples employing the scales. Once the procedure is clearly under- stood, the analysis can be quite rapid, with a good measure of accuracy. EXAMPLE 6.19 Determine the quiescent values of ID and VGS for the network of Fig. 6.59. Figure 6.59 Example 6.19. Solution Calculating the value of m, we obtain VP 3 V m 0.31 IDSSRS (6 mA)(1.6 k ) The self-bias line defined by RS is plotted by drawing a straight line from the origin through a point defined by m 0.31, as shown in Fig. 6.60. The resulting Q-point: ID VGS 0.18 and 0.575 IDSS VP 292 Chapter 6 FET Biasing VCC RC RB Io C Vo C Vo Ii Ii Io C2 B B Vi Vi Zo RC C1 Zo RB E Zi E Zi Figure 8.1 Common-emitter fixed-bias con- Figure 8.2 Network of Figure 8.1 following figuration. the removal of the effects of VCC, C1, and C 2. Ii Ib Ic b c + + Zi Io Vi re Ib Vo RB ro RC Figure 8.3 Substituting the re – – model into the network of Fig. Zo 8.2. The next step is to determine , re, and ro. The magnitude of is typically ob- tained from a specification sheet or by direct measurement using a curve tracer or transistor testing instrument. The value of re must be determined from a dc analysis of the system, and the magnitude of ro is typically obtained from the specification sheet or characteristics. Assuming that , re, and ro have been determined will result in the following equations for the important two-port characteristics of the system. Zi: Figure 8.3 clearly reveals that Zi R B re ohms (8.1) For the majority of situations RB is greater than re by more than a factor of 10 (recall from the analysis of parallel elements that the total resistance of two parallel resistors is always less than the smallest and very close to the smallest if one is much larger than the other), permitting the following approximation: Zi re ohms (8.2) RB 10 re Zo: Recall that the output impedance of any system is defined as the impedance Zo determined when Vi 0. For Fig. 8.3, when Vi 0, Ii Ib 0, resulting in an open-circuit equivalence for the current source. The result is the configuration of Fig. 8.4. Zo ro RC Zo R C ro ohms (8.3) If ro 10 RD, the approximation RC ro RC is frequently applied and Zo RC (8.4) Figure 8.4 Determining Zo for ro 10RC the network of Fig. 8.3. 8.2 Common-Emitter Fixed-Bias Configuration 339