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Lecture 12 Transistor Bias Section 5.1-5.2

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K-30/AK-710 FM Wireless Microphone Audio Amplifier Radio Frequency Oscillator Radio Frequency Amplifier

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Operating Point Analysis and Design

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Simple Biasing Assumed VBE and β → IB→IC →VC Comments: IB is sensitive to VBE. IC is very sensitive to β.

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Iteration Solution IC=βIBIC=βIB (Kick off iteration with VBE=0.7)

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Example 1 IterationVBEIB (uA)IC (mA) 10.711.31.8 20.683411.3171.8 30.683411.3171.8 Assumed: RB=1 Mohms RC=2 Kohm IS=6.734e-15 Beta=155

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ADS Simulation IB=11.3 uA IC=1.76 mA Beta=155 ParameterADSIteration VBE674 mV683.4 IB11.3 uA11.317 uA IC1.76 mA1.8 mA

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Execute Iterations in Matlab

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β Variation ParameterΒ=100Β=155 VBE672.1 mV 683.4 mV IB11.328 uA 11.317 uA IC1.1 mA1.8 mA gm43.6 mS69.2 mS Variation of gm implies that the gain of the amplifier will vary significantly as a function of beta.

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Resistive Divider Biasing

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Back of the Envelope Calcuation Assume the base current is negligible, i.e. negligible compared to the current in R1. IC does not depend on Beta!

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Negligible Base Current V BE =R 3 /(R 1 +R 3 )V CC V BE =5.75/(5.75+17)2.5V=0.631 V I(R1)/IB=110uA/2.10=52.38

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Sensitivity to Component Variation Nom.1%5% R2 (KOhm) 5.755.80756.037 VBE (mV)623626639 IB (uA)2.102.353.59 IC (uA)229262424 Gm (mS)8.810.116.3 1% error in R2 leads to 14 % error in IC. 5% error in R2 leads to 85 % in IC.

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Biasing with Emitter Degeneration If R2↑→VP↑→IE↑→VRE↑→small ∆V BE →Small ∆I C An error in VX due to inaccuracies in R1, R2 and VCC is absorbed by RE, leading to a smaller change in VBE.

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Design Rules V RE should be > 100 mV.

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ADS Simulation IB=12.4 uA IC=1.91 mA Beta=154

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Sensitivity to Component Variation Nom.1%5% R3 (KOhm) 6.86.8687.140 VBE (mV)0.68 IB (uA)12.412.513.1 IC (mA)1.911.932.02 Gm (mS)73.574.277.7 1% error in R2 leads to 1.05 % error in IC. 5% error in R2 leads to 5.7 % error in IC.

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Misc.

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What if base current is not ignored!

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Iterative Method Initial assumption: VBE=0.7 V

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