How to Bias BJTs for Fun and Profit

Transcription

1 How to Bias BJTs for Fun and Profit Standard BJT biasing configuration: The standard biasing configuration for bipolar junction transistors, sometimes called the H-bias configuration because the resistors form the outline of the letter H, is shown in Figure 1 below. This configuration can be used for all BJT amplifiers (common emitter, common base, and common collector), although in the common-collector configuration we usually set R C 0. V CC 1 R 1 R C C B V BE V CE E C V B R 2 V E R E Figure 1. Standard BJT biasing configuration. Biasing procedure: Biasing a BJT means establishing the desired values of V CE and C so that the amplifier will have the proper gain, input impedance, undistorted output voltage swing, etc. These values of V CE and C are known as the quiescent operating point or Q-point. The values of V CE and C required are determined

2 2 from inspection of the BJT's data sheet and load line analysis. β Since E β 1 (1) and β >> 1, we have E as shown in the figure above. We will assume E to bias the transistor. The bias configuration shown above actually sets the value of E. Each resistor in the configuration shown above plays a role in biasing the transistor. n addition, R C also sets the output resistance of common-emitter amplifiers, as can be seen in Figure 2 below, which is the small-signal equivalent circuit (valid at frequencies where the parasitic capacitances of the BJT are negligibly small and if R E is bypassed by a suitable capacitor) of the amplifier shown in Figure 1 above. i b v i R B r π β i b r o R C v o Figure 2. The AC small-signal equivalent circuit of the amplifier shown in Figure 1. This AC equivalent circuit is not used for DC biasing!! n Figure 2, RB R1 R2. f v i 0 (the condition for calculating output resistance), then i b 0, the controlled current source is off (i.e., it is an open circuit), and the output resistance is r R. However, ro 10 kω >> RC, so r o can be neglected and the output resistance is approximately R C. f the output impedance of a common-emitter amplifier is a critical design specification, set R C first. However, make sure that RC 3VCC 4 VCE. f this cannot be achieved at the desired Q-point, a new Q-point must be selected. o C The only purpose of R E is to provide DC feedback to stabilize the Q-point against variations in the β

3 3 (also known as h FE ) of the BJT. Since β can vary by as much as five to one from one BJT to another (even if the BJTs have the same 2N number), large unit-to-unit variations in Q-point could result unless this DC feedback is present. When the resistor values in the above figure are selected properly, β variations will have a negligibly small effect on the Q-point. nstead, unit-to-unit variations in Q-point will be due almost entirely to resistor tolerance. The voltage V E across R E sets E, which is approximately equal to C. To provide sufficient feedback, V E is usually chosen to be one-quarter to one-third of V CC. Because V BE 0.7 V (silicon devices), V E is set by the voltage divider formed by R 1 and R 2. However, the alert reader will note from Figure 1 above that R 1 and R 2 are not in series, and hence do not form a voltage divider! Only if the maximum value of B is much less than 1, so that B can be neglected, will R 1 and R 2 act like a voltage divider. The circuit designer must establish this condition by the appropriate choice of values for R 1 and R 2. BJT biasing example: Consider a 2N3904 BJT with V CC 10 V and a desired value of V CE 4.0 V. Assume that the output resistance of the amplifier is not critical. From the data sheet for the 2N3904 we find that maximum DC current gain occurs when C is in the range of 3 to 10 ma. With no specification on amplifier bias current to concern us, we select C 5 ma. Our Q-point, therefore, is V CE 4.0 V and C 5 ma. Also from the data sheet, we see that at this Q- point, the minimum specified DC current gain is β min 100. Since there is no specification on output resistance, we will determine the value of R E first. We apply the engineering rule of thumb given above and select V E V CC V. (2)

4 4 But VE ERE RE, so R E VE C 066. kω. (3) We select the closest standard value, or R E 680 Ω. (4) To find R C, we use Kirchhoff's voltage law (KVL) to get ( ) VCC VCE RC RE. (5) The only unknown in eq. (5) is R C, so we solve for R C and get R C VCC V CE RE kω. (6) 5 We use the closest standard value, R C 510 Ω. To achieve V E 3.3 V [eq. (2)], we must have VB VBE VE V. (7) Now, to make the combination of R 1 and R 2 act like a voltage divider, we must make the largest possible value of B, i.e., Bmax, negligibly small compared to 1. Since B C, (8) β

5 5 B max C. (9) β min We must have 1 much larger than this, so we set 1 20B max 20 β min. (10) Now that we have designed our circuit such that B is negligibly small even under the worst-case condition of minimum β, we can pretend that there is no connection between R 1 and R 2 and the base of the BJT. n that case, 1 VCC R R C, (11) β min V or R R CC 1 2 β min. (12) 20 But, from the voltage divider, we must also have R2 R R V CC V B 40. V (13) 1 2 from eq. (7). We use the limiting equality in eq. (12) to write eq. (13) as 20R2 VB. (14) β min We solve for the unknown R 2 : R 2 ( 100)( 4.0) ( )( ) βminv B 4.0 kω. (15) C Finally, again using the limiting equality in eq. (12), we solve eq. (12) for the only remaining unknown

6 6 resistor value, R 1 : R min CC 1 R2 ( 100)( 10) ( )( ) β V kω. (16) Since neither 4.0 kω nor 6.0 kω is a standard value, we select the next smaller [so that the inequality in eq. (12) will be satisfied] standard values, R kω and R kω. To confirm that the BJT is biased at the chosen Q-point, we redraw Figure 1 in the form shown in Figure 3. V CC R 1 B R C C V CC V B R 2 V BE V E V CE E C RE Figure 3. An equivalent way of drawing the circuit of Figure 1. We take the Thevenin equivalent circuit looking from the base of the BJT toward R 1 and R 2 to convert this figure to the equivalent form:

7 7 V CC R C C B V TH R TH V BE V E V CE E C R E Figure 4. The standard BJT biasing configuration with the base-bias circuit replaced by its Thevenin equivalent. n Figure 4, ( 5.6)( 3.9) RR R 1 2 TH R1 R2 2.3 k R1 R Ω (17) R 3.9 CC V R1 R and V 2 V ( ) TH. (18) We apply Kirchhoff s voltage law around the base-emitter loop to get VTH BRTH VBE E RE 0. (19) We use eq. (8) to eliminate B from eq. (19) and E β 1 β (20) to eliminate E. We solve the result for C and get

8 8 β VTH VBE RTH ( β 1) RE. (21) f we assume β β min 100 for the 2N3904, eqs. (4), (17), and (18) substituted into eq. (21) give us C ( 100) 4.8 ma ( )( ), (22) only 4 percent less than the desired value of 5 ma. We substitute this value of C, the value of R E from eq. (4), and the value of R C (510 Ω) into eq. (5) and solve for V CE to get ( ) ( )( ) VCE VCC RC RE V, (23) 7.5 percent more than the desired value. Modified bias configuration: n high-frequency amplifiers R C might be replaced by an inductor. n common-collector amplifiers (also known as emitter followers) R C is frequently replaced by a short circuit. n either case, R C 0 in DC biasing calculations. We will repeat the above example for the case when R C 0. n this case, we do not get to choose V E. nstead, with R C 0, eq. (5) reduces to VCC VCE RE. (24) Since we determined V CE and C when we selected the Q-point, the only unknown in this equation is R E. We solve eq. (24) for R E and get

9 9 RE VCC VCE kω, (25) which coincidentally is a standard value. We now have ( )( ) VE RE V, (26) and the rest of the design proceeds as above. Biasing without an emitter resistor: Sometimes amplifier stability considerations or the lack of space force the designer to bias a BJT without an emitter resistor. The only purpose of the emitter resistor is to provide negative DC feedback to stabilize the circuit against β variations. f the circuit has no emitter resistor, the required negative feedback must be provided another way, such as shown in the following circuit: V CC 1 R C CC R 1 C B V B R 2 V BE V CE Figure 5. Biasing without an emitter resistor.

10 10 Note from Fig. 5 that VB VBE 0.7 V (27) and C 1. (28) Once again, we design the circuit such that Bmax << 1 so that B can be neglected. This requires the use of eq. (11) again: 1 20 C. (11) βmin With B negligible, we have VB VBE 1R2 or, once we have chosen 1 with the aid of eq. (11), R2 V BE 1 (29) With B negligible, we see from Fig. 5 that ( ) VCE 1 R1 R2, (30) V or R CE 1 R2 1. (31) Finally, to calculate R C we use eq. (28) and Ohm s Law to derive VCC V CE CC 1, RC

11 11 or RC VCC VCE 1. (32) Unfortunately, this biasing scheme is sensitive to temperature variations. To show this, we rewrite eq. (29) as 1 V BE R2. (33) Substituting this into eq. (30) gives R1 R2 R V 1 CE VBE 1 VBE R2 R2. (34) Since V BE varies 2.2 mv/ºc, V CE will vary by the factor 1 R 1 /R 2 greater than this. This could be an unacceptable variation in a system that must function from 30ºC to 70ºC. Usually, the emitter resistor must be eliminated to insure AC stability only in UHF, microwave, and millimeter-wave circuits. n such circuits the BJT being biased is often relatively expensive (> $0.50 each). Therefore it can be cost-effective to use a low-cost, low-frequency BJT to bias the high-frequency BJT. Such a scheme is shown in the following figure: 1 V CC R 1 B2 C2 R x CC R 2 V y R B Q 2 R C B1 C1 V x Q 1 V CE Figure 6. Active biasing of a BJT without an emitter resistor.

12 12 n this circuit, the BJT being biased is Q 1. The only function of the low-cost, low-frequency pnp BJT Q 2 is to provide the base bias current B1 to Q 1. The negative feedback in this circuit occurs as follows: f something causes C1, the collector current in Q 1, to increase, the voltage V x decreases (because the voltage drop across R x increases due to the increased collector current). However, the voltage V y is fixed by the voltage divider formed by R 1 and R 2. Therefore the base-emitter voltage of Q 2 decreases, reducing Q 2 s collector current C2, which is also the base current B1 to Q 1. The reduction of B1 returns C1 to its original value. A very small change in C1 can produce a relatively large change in C2 B1 due to the exponential relationship V between base-emitter voltage and collector current in Q 2 ( BE2 V e T ). To design this bias circuit, note that C2 S C B1 (35) since C2 B1. But B1 << C1, so C 1. (36) Therefore VCE VCC ( RC Rx ) 1. (37) The value of R x can be determined from Vy VEB2 VCC Rx1. (38) Do not, however, make R x so large that the desired V CE cannot be achieved. n many cases R B can be eliminated since the resistance looking into the collector of Q 2 is large.