In this assignment, you will design a differential amplifier as shown in the schematics below.
Your design should satisfy the required differential gain, input impedance, singleended commonmode
gain, and the power dissipation specifications provided in Section A below. Then in Sections B and C, you
will simulate your circuit on LTSpice to compare the simulation results with hand calculations.
A. Hand design: Design the bipolar differential amplifier and the current source and bias network
(π
1, π3, πππ π4) above such that:
(i) Differential gain: π΄π β₯ 200 π,
π
(ii) Input differential resistance: π
ππ β₯ 50 πΞ©,
(iii) π΄ππ < 0.1 where π΄ππ is the singleended commonmode gain, defined as the gain for a common
mode input signal when the output is measured from one of the outputs with respect to ground, rather
than differentially.
(iv) To maximize battery life, the power consumption of the differential amplifier, πππππ΄πΏ, must be less
than 2 milliwatts.
Design Suggestion for Part A.
1. Derive the expression for π
, ignoring π of Q1 and Q2.). Replace small signal parameters with
ππ π
βDC currentsβ, βresistorsβ, βπ β, βπ½β, βπ β, etc., use specific values (e.g., π = 100 π, π½ = 200,
π‘hπ΄ π΄
etc.), and simplify the expressions. The π
ππ design specification will help determine an upper limit
for the DC collector current of Q1 (and Q2 since πΌπΆ1 = πΌπΆ2).
2. The total power dissipation is π
ππππ΄πΏ
=π +π =9πΓ(πΌ +πΌ ). Here, πΌ is the
ππ·π· πππ ππ·π· πππ ππ·π·
sum of all DC currents leaving the +π
π·π·
and πΌ is the sum of all dc currents entering the βπ .
πππ ππ
Express πΌππ·π· and πΌπππ in terms of the collector currents of Q1 (or Q2), ignoring the current in the
reference current generation branch formed by π
1 and π4. The πππππ΄πΏ design specification will
help determine another upper limit for πΌπΆ1 = πΌπΆ2.

Derive expressions for π΄ and π΄ . When deriving π΄ , include π of Q1 or Q2. When deriving π΄
πππππ ππ
ignore π of Q1 and Q2 but include π of Q3. Replace small signal parameters with βDC currentsβ,
ππ
βresistorsβ, βπ β, βπ½β, βπ β, etc., use specific values (e.g., π = 100 π, π½ = 200, etc.), and
π‘hπ΄ π΄
simplify the expressions. The π΄π and π΄ππ design specifications will respectively provide lower and
upper limits for the product π πΆ Γ πΌπΆ1. 
Consider the forwardactive region requirement of Q1 (or Q2). For π = 0 π, find another upper
πΆπ
limit for the product π πΆ Γ πΌπΆ1. 
Pick an πΌπΆ1 satisfying all upper limits for πΌπΆ1 found in steps 1 and 2. Find π
1 based on the value you
pick for πΌπΆ1. Pick an π πΆ satisfying the upper and lower limits for π πΆ β πΌπΆ1 found in steps 3 and 4.
Inyoursimulations,usetheBJTmodel2N2222ofNXP,whichhasaSPICEmodelasbelowwithπ andπ½
highlighted:
π΄
B. DC Analysis: In LTSpice do a DC operating point simulation (.op) with both inputs connected to ground
(i.e.,π =0π).DeterminethesimulatedDCvaluesforπΌ ,πΌ ,πΌ ,πΌ ,πΌ ,π ,π ,π ,π .Compare
πΆπ π
1πΆ3πΆ4πΆ1πΆ2 π΅3 πΈ1,2 π1 π2
these results with your hand calculations. Additionally, comment on the matching between πΌπ
1 πππ πΌπΆ3
and comment on the calculated vs. simulated match between πΌπ
1 πππ πΌπΆ3.
C. Transient Analysis: In LTSpice do a transient simulation (.tran) for 100 ms.
For differential smallsignal input simulations:
Apply π£ =1ππ π πππ’π ππππππ πππππππ‘100π»π§. [i.e., π£ =+π£ππ =0.5ππsin(2βπβ100π»π§βπ‘)
ππ π ππ1
2
andπ£ππ2 =βπ£ππ =0.5ππsin((2βπβ100π»π§βπ‘)+π)withDCoffset=0V.]
2
π£ =π£ =π£
πππ1 πππ2 ππ
For commonmode smallsignal input simulations:
Apply π£ =1ππ π πππ’π ππππππ πππππππ‘100π»π§. [i.e.,
=1ππsin(2βπβ
ππ π
100π»π§ β π‘) with DC offset = 0V.]
1. For the differential smallsignal input, what is the expected emitter voltage of Q1 and Q2,
π£π1(= π£π2)? Plot the simulated waveform. What is the simulated value of π£π1(= π£π2)?
2. Plot π£ππ, π£ππ(π£ππ = π£π2 β π£π1), πππ πππ. Note that πππ is the base current of Q1 (πππ = ππ1).
Calculate the simulated π΄π = π£ππ /π£ππ and π
ππ = π£ππ /πππ . Compare the values with your
design targets.
3. If the simulation results do not match the design constraints, revisit your design to achieve
the targets.
4. For the commonmode smallsignal input, plot π£ππ and π£πππ . (π£πππ = π£πππ2 =
π£πππ1 π€hππ π‘hπ ππππ’π‘ ππ π ππππππ β ππππ π πππππ)
Report Requirements
A. Your hand calculations for part A must be detailed and sequential. Show every step of the derivations
clearly, and explain how and why you select each parameter, including any approximations made.
B and C. For parts B and C, besides answering the questions and plotting the requested simulation results,
complete the table below. Provide explanations for any discrepancies exceeding 10%.
πΌπ 1 πΌπΆ4 πΌπΆ3
πΌπΆ1 πΌπΆ2
Hand
calculations
Simulated
Percent
discrepancy
Hand
calculations
Simulated
Percent
discrepancy
πππππ΄π
π΄
π΅3 πΈ1,2 π1 π2 π ππ ππ