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# thebjt - The BJT BJT Device Equations Figure 1 shows the...

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The BJT BJT Device Equations Figure 1 shows the circuit symbols for the npn and pnp BJTs. In the active mode, the collector-base junction is reverse biased and the base-emitter junction is forward biased. Because of recombina- tions of the minority and majority carriers, the equations for the currents can be divided into three regions: low, mid, and high. For the npn device, the currents are given by Low Level: i B = I SE · exp μ v BE nV T 1 ¸ (1) i C = I S · exp μ v BE V T 1 ¸ (2) Mid Level: i B = I S β F · exp μ v BE V T 1 ¸ (3) i C = I S · exp μ v BE V T 1 ¸ (4) High Level: i B = I S β F · exp μ v BE V T 1 ¸ (5) i C = I S r I K I SO · exp μ v BE 2 V T 1 ¸ (6) where all leakage currents that are a function of v CB have been neglected. In the current equations, I S is the saturation current and β F is the mid-level base-to-collector current gain. These are functions of the collector-base voltage and are given by I S = I SO μ 1 + v CB V A = I SO μ 1 + v CE v BE V A (7) β F = β FO μ 1 + v CB V A = β FO μ 1 + v CE v BE V A (8) Figure 1: BJT circuit symbols. In the equations for i B and i C , V A is the Early voltage and I SO and β FO , respectively, are the zero bias values of I S and β F . The constant n is the emission coe cient or ideality factor of the base-emitter junction. It accounts for recombinations of holes and electrons in the base-emitter 1

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junction at low levels. Its value, typically in the range 1 n 4 , is determined by the slope of the plot of ln ( i C ) versus v BE at low levels. The default value in SPICE is n = 1 . 5 . The constant I SE is determined by the value of i B where transition from the low-level to the mid-level region occurs. The constant I K is determined by the value of i C where transition from the mid-level to the high-level region occurs. Note that I S / β F = I S 0 / β F 0 so that i B is not a function of v CB in the mid-level region. The equations apply to the pnp device if the subscripts BE and CB are reversed. Figure 2 shows a typical plot of i C versus v BE for v CE constant. The plot is called the transfer characteristics. There is a threshold voltage above which the current appears to increase rapidly. This voltage is typically 0 . 5 to 0 . 6 V. In the forward active region, the base-to-emitter voltage is typically 0 . 6 to 0 . 7 V. Figure 3 shows typical plots of i C versus v CE for i B constant. The plots are called the output characteristics. Note that the slope approaches a constant as v CE is increased. If the straight line portions of the curves are extended back so that they intersect the v CE axis, they would intersect at the voltage v CE = V A + v BE ' V A . For v CE small, v BE > v CE and the BJT is in the saturation region.
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thebjt - The BJT BJT Device Equations Figure 1 shows the...

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