Part I Pre-lab, Problem (a)

Using the rule of thumb that VG ≈ VD/3 > VT, choose R1= 1 MΩ and R2= 470 kΩ. This gives VG as:

𝑉𝐺 =𝑅2

𝑅1 + 𝑅2𝑉𝐷𝐷 = 4.8𝑉.

Then Rin = R1 || R2 = 319.7 kΩ > 200 kΩ, so input resistance spec is satisfied.

If Vt=1.7V, and the drain current is chosen to be small ≈0.3 mA then VGS – Vt = VG – VS – Vt ≈ 0 (from the saturation region equation) so that

Vs ≈ VG – Vt = 4.8 – 1.7 ≈ 3.0 V.

Then choosing RS = 10 kΩ gives ID as

𝐼𝐷 =𝑉𝑆𝑅𝑆

= 0.3 𝑚𝐴.

Now compute the transconductance gm at the operating point ID as:

𝑔𝑚 = �2𝑘𝑛𝐼𝐷 = √2 × 0.02 × 0.0003 = 0.00346 𝐴/𝑉.

The mid-band gain G is now calculated as:

𝐺 = −𝑔𝑚𝑅𝑜 = −50 = −0.00346 × 𝑅𝑜,

which gives the output resistance RO as:

𝑅𝑜 = 14.45 𝑘𝛺.

Now compute the NMOS output resistance ro:

𝑟𝑜 = 𝑉𝐴𝐼𝐷

= 1000.3𝑚𝐴

= 333 𝑘𝛺 → 𝑟𝑜||𝑅𝐿 = 76.9 𝑘𝛺.

This gives the drain resistance RD as

𝑅𝐷 = 11𝑅𝑜

− 1𝑟𝑜||𝑅𝐿

= 17.8 𝑘𝛺.

Choosing 𝑅𝐷 = 22𝑘𝛺 should give a gain magnitude | G | > 50 V/V.

At 𝑅𝐷 = 22𝑘𝛺, we expect

VD = VDD – ID × RD = 15 – .0003 × 22000 = 8.4 V.

This value of VD is reasonably close to 9V, which is the midpoint between VS = 3 V and VDD = 15 V. We want VD near this midpoint to ensure maximum output voltage swing of about 12 V p-p.

2

AC 1

Rser=50

V1

M1

nmos_enhancement_mosfet

Rser=50

V2

15

C1

10µ

C2

10µ

C3

47µ

R11Meg

R2470K

R322K

R410K

R5100K

.model nmos_enhancement_mosfet nmos (kp=100u Vto=+1.7V lambda=0.01 L=1u W=200u)

.ac dec 100 1 1000Meg

Note that K = kp*(W/L) in LTSPICE. If you fix kp=100u, you should choose W and L so that K comes out to your desired value.Ctrl-RightClick on the mosfet to set its value to nmos_enhancement_mosfet

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