Lab 1
Part 1
LPF
Transient analysis of a low pass filter
1. First of all to make the tau = 0.5ns
We should make r = 1k ohm and c = 0.5ps
Red is vout
Green is vin
Purple is the current
2.Rise time (10% to 90%) and fall time (90% to 10%) were
calculated using Cadence calculator expressions and exported to
ADEXL:
• riseTime(VT("/vout") 0 nil 1 nil 10 90 nil "time")
• fallTime(VT("/vout") 1 nil 0 nil 90 10 nil "time")
parametric sweep (fall & rise) time
First rise & fall time analytically :
t_r = t_f = τ × ln(9) = RC × ln(9) ≈ RC × 2.197
With R = 1 kΩ and C = 0.5 pF (as simulated, giving τ = 0.5 ns):
t_r = 0.5 ns × 2.197 ≈ 1.099 ns
parametric sweep graph :
We can see here that Higher RL slows the charging/discharging
of CL, causing the output to lag the input more. The output
amplitude also decreases since T_high/τ ratio decreases.
Bode plot : (using db 20 function)
Band width(3db) calculation and gain :
For a first-order RC LPF, the analytical -3dB bandwidth is:
f_-3dB = 1 / (2π × R × C)
With R = 1 kΩ and C = 0.5 pF:
f_-3dB = 1 / (2π × 1000 × 0.5×10⁻¹²) ≈ 318.3 MHz
parametric sweep for r :
Comments on AC Parametric Sweep Results:
• Bandwidth decreases inversely with RL (f ∝ 1/R): RL = 1 kΩ
→ BW = 317.6 MHz; RL = 10 kΩ → BW = 31.76 MHz; RL =
100 kΩ → BW = 3.176 MHz; RL = 1 MΩ → BW = 317.6 kHz.
• The Bode magnitude plots shift left (lower cutoff) as RL
increases, but the DC gain remains constant at 0 dB (unity
gain) for all values — as expected for a passive RC filter.
• The BW vs. RL plot shows a hyperbolic (1/R) relationship.
Each decade increase in RL results in a decade decrease in
bandwidth, following f_-3dB = 1/(2πRC).
Part 2
Mosfet
Random no for w/l :
Screenshot of short and long channel of nmos :
The long channel device carries higher drain current. This is
because the two device types follow different current laws:
• Long channel: ID ∝ (VGS − Vth)² — the current is quadratic
in overdrive voltage
• Short channel: ID ∝ (VGS − Vth)¹ — the current is linear in
overdrive voltage due to velocity saturation
The relationship is quadratic between the id and vgs in
short channel and near linearity in long channel and that is
because of the velocity saturation.
id vs vgs in pmos transistor :
Id in pmos and nmos transistor in both short channel and long
channel :
 we can see that NMOS produces significantly higher drain
current than PMOS for the same dimensions.
 this is because of the mobility as the electron mobility is
higher than the hole mobility.
 The ratio between the nmos and pmos current is nearly 4.5
as we can deduce it from the graph above.
 We can see also that the nmos is more affected by the
channel length as the current in pmos did not change a lot
Gm vs vgs :
NMOS is more affected to short channel effects (SCE) such as:
• Velocity saturation: Higher electron mobility means the
critical lateral field for velocity saturation is reached at
shorter channel lengths, amplifying SCE in NMOS.
• DIBL (Drain-Induced Barrier Lowering): NMOS exhibits
larger threshold voltage shifts with VDS due to stronger shortchannel electrostatics.
• yes gm does saturate at both long and short channel but it
appeared heavily in the green curve (long channel).
• the blue curve(short channel) also saturate at a point but as
soon as it reaches saturation it starts to decrease.
• due to velocity saturation, the derivative ∂ID/∂VGS approaches
a constant (gm ≈ W·Cox·vsat), which no longer increases with
VGS
vds and vgs dc sweep :
Dc sweep long and short channel :
 Short channel is blue
 Long channel is red
We can see that :
 Short channel has higher current than the long channel as
The shorter channel length L means a larger W/L ratio,
which directly increases ID.
 The long channel has higher slope in saturation as we can
see that the red lines are continuing to grow while the red
are not.
 Since λ ∝ 1/L, the long channel has a smaller λ, which means
higher ro — so it should actually have a flatter curve in
saturation.
 But the additional reason for the steeper slope in the long channel
is DIBL (Drain Induced Barrier Lowering) — wait, that's a
short channel effect.