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# Impedance Transformation

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1. Impedance Transformation

2. Resistance of Inductor • R=Rsh(L/W) • Rsh is the sheet resistance • Rsh is 22 mOhms per square for W=6um. • If the outer diameter is 135 um, the length is approximately 135um x4=540 um. • R=22 mOhms x (540/6)=1.98 Ohms Q=(ωL)/R=(2π2.4G0.336 nH)/1.98 Ω=2.56

3. Include Resistor In the Tank Circuitry Q=2.427/(3.076-1.888)=2.04 Inclusion of parasitic resistance reduces the circuit Q from 10.

4. Problem • The gain drops significantly when the resistive loss in the inductor is accounted for.

5. Assignment • Redesign the circuit so that it meet the following specifications: • fo=2.4 GHz • Q(circuit quality factor)>7 • Av=Vout/Vin=-6 dB • Rs=50 Ohms

6. Design Constraints • Design constratins: • Av=Rp/(Rs+Rp) • Rp=Rind(1+Qind*Qind) • Qcirc=ωo(Rp*Rs/(Rp+Rs))C=ωoAvRsC • ωo=1/sqrt(LC) • Qind=ωoL/Rind

7. Submission Check List • Determine the Qind that achieves the Av. • Submit the circuit schematic • Submit AV as a function of frequncy from 1M to 10 GHz.