The f H and f Z . f H = 39.78 MHz f Z = 159.10 GHz Given Information: g m = 3 mA/V C g s = 25 fF C g d = 5 fF C L = 30 fF R s i g = 10 k Ω R L ' = 20 k Ω Calculation: Write the expression for the time constant of the capacitance C g s as τ g s = C g s R s i g Plugging the values τ g s = 25 fF 10 k Ω τ g s = 25 × 10 − 12 s Write the expression for the time constant of the capacitance C g d as τ g d = C g d R s i g 1 + g m R L ' + R L ' Plugging the values τ g d = 25 fF 10 k Ω 1 + 3 mA/V 20 k Ω + 20 k Ω τ g d = 3150 × 10 − 12 s Write the expression for the time constant of the capacitance C L as τ C L = C L R L ' Plugging the values τ C L = 30 fF 20 k Ω τ C L = 600 × 10 − 12 s Write the expression for the total time constant as τ H = τ g s + τ g d + τ C L Plugging the values τ H = 250 × 10 − 12 s + 3150 × 10 − 12 s + 600 × 10 − 12 s τ H = 4000 × 10 − 12 s τ H = 4 ns Write the expression for 3-dB frequency f H in terms of time constant τ H as f H = 1 2 π τ H Plugging the values f H = 1 2 π 4 ns f H = 39.78 MHz Write the expression for zero transmission frequency f Z in terms of trans-conductance g m and capacitance C g d and C g s f Z = g m 2 π C g d + C g s Plugging the values f Z = 3 mA/V 2 π 5 fF + 25 fF f Z = 3 mA/V 2 π 30 fF f Z = 159.10 GHz

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Chapter 10, Problem 10.40P

To determine

The fH and fZ .

fH=39.78 MHzfZ=159.10 GHz

Given Information:

gm=3 mA/VCgs=25 fFCgd=5 fFCL=30 fFRsig=10 kΩRL'=20 kΩ

Calculation:

Write the expression for the time constant of the capacitance Cgs as

τgs=CgsRsig

Plugging the values

τgs=25 fF10 kΩτgs=25×10−12 s

Write the expression for the time constant of the capacitance Cgd as

τgd=CgdRsig1+gmRL'+RL'

Plugging the values

τgd=25 fF10 kΩ1+3 mA/V20 kΩ+20 kΩτgd=3150×10−12 s

Write the expression for the time constant of the capacitance CL as

τCL=CLRL'

Plugging the values

τCL=30 fF20 kΩτCL=600×10−12 s

Write the expression for the total time constant as

τH=τgs+τgd+τCL

Plugging the values

τH=250×10−12 s+3150×10−12 s+600×10−12 sτH=4000×10−12 sτH=4 ns

Write the expression for 3-dB frequency fH in terms of time constant τH as

fH=12πτH

Plugging the values

fH=12π4 nsfH=39.78 MHz

Write the expression for zero transmission frequency fZ in terms of trans-conductance gm and capacitance Cgd and Cgs

fZ=gm2πCgd+Cgs

Plugging the values

fZ=3 mA/V2π5 fF + 25 fFfZ=3 mA/V2π30 fFfZ=159.10 GHz

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