Section D10: Compensation

In the previous section, we looked at how four parameters (VCC, VBE, ICBO, and β) can affect the total collector current and, therefore, the Q-point of the . Diode compensation is a technique that is used to reduce the Q-point variations by selecting a diode that has temperature characteristics similar to the . To make sure that the diode and transistor have the same temperature characteristics, we can use a BJT with the same specifications as the amplifier transistor that is diode-connected. This simply involves shorting the collector to the base as shown in the figure to the right for an npn BJT (this can also be done with pnp BJTs). As a reminder, the diode symbol and the model for the forward biased diode are also shown to the right œ remember that the current flows in the direction of the arrow and that, unless an ideal diode is specified, the diode forward resistance and turn-on must be included in all calculations.

The diode is connected in the base circuit of the amplifier as shown in Figure 7.9a, reproduced to the right. The addition of the diode in this manner allows temperature compensation since the VON of the diode varies in the same fashion as the VBE of the transistor. If the used in the amplifier and to construct the diode are matched, the diode characteristics and base- emitter junction characteristics will be the same. Under these circumstances, variations in VBE due to changes in bias parameters will effectively be significantly reduced or cancelled. Including the complete diode model and writing the KVL around the loop indicated in red, we get the new bias equation for the base to ground voltage as

VB = VON + I D R f + I D R1 = I C RE +VBE . (Equation 7.23)

Using the same figure, and writing a KVL for the path indicated in blue, we get (approximating IC≈IE=ID):

VCC = I D R2 +VON + I D R f + I D R1 .

This expression may be rearranged to solve for the diode current ID:

VCC −VON I D = . (Equation 7.24) R1 + R2 + R f

Defining the Thevenin equivalent voltage as from base to ground represented by the first summation in Equation 7.23 (we called it VBB earlier), substituting Equation 7.24 for ID, and assuming that Rf << R1,

VCC R1 +VON R2 VTH = . (Equation 7.26) R1 + R2

The expression for the Thevenin equivalent resistance (RB) remains unchanged if Rf << R1:

RTH = R1 || R2 . (Equation 7.26)

The equivalent base circuitry for the diode compensated configuration is shown to the right (Figure 7.9c). Reflecting the Thevenin resistance down to the emitter circuit by dividing by β (assuming β>>1, β+1≈β), and writing a KVL around the loop assuming IC+IE,

R V = V + I TH + I R . TH BE C β C E

Rearranging this relationship to solve for IC, expressing it as the quiescent value ICQ, and substituting Equation 7.26 for VTH:

(V R +V R ) CC 1 ON 2 −V (R + R ) BE I = 1 2 . (Equation 7.28) CQ R TH + R β E

The sensitivity of the diode compensated circuit configuration to temperature variations is defined by taking the partial derivative of Equation 7.28 with respect to temperature. From our discussions of the last section, the temperature dependent parameters in Equation 7.28 are VON and VBE.

If R2 >> R1, this partial derivative may be simplified to

≈ ’ ∆ ÷ ∂I ≈ ∂V ∂V ’ 1 C = ∆ ON − BE ÷∆ ÷. (Equation 7.30) R ∂T « ∂T ∂T ◊∆ TH + R ÷ « β E ◊

If R1 ≈ R2, better compensation may be achieved by using two in series. The derivation of appropriate equations is the same as above except now we have two diodes to consider. Under the assumption that Rf1 and Rf2 << R1, the expression for ICQ is modified to be

(V R + 2V R ) CC 1 ON 2 −V (R + R ) BE I = 1 2 . (Equation 7.31) CQ R TH + R β E

The expression for the circuit sensitivity will unchanged and will be the relationship defined in Equation 7.30.

Note that if the amplifier transistor and the diode-connected transistor are perfectly matched, δVON/δT will be exactly equal to δVBE/δT and temperature will have no effect on the collector current (and therefore on the Q-point). There may still be some dependence on β and VCC, but this is a major step in ensuring consistent amplifier behaviors!