## Description

Common-emitter versus common-source amplifier

** **Figure 1a. Common-emitter (CE) amplifier Figure 1b. Common-source (CS) amplifier

For the following, *T* = 300K, *V _{A}* = 100V,

*V*−

_{GS}*V*= 500mV, = 0.1V

_{th}^{-1},

*C*= 10pF and

_{L}*I*=

_{C}*I*= 1mA.

_{D}- Calculate the DC voltage gain
*v*/_{out}*v*for each structure. Determine the ratios_{in}*g*/_{m}*I*and_{C}*g*/_{m}*I*(transconductance efficiency)._{D} - For each structure, determine the small-signal transfer function
*v*/_{out}*v*as a function of frequency. Plot the Bode magnitude and phase (by hand or using MATLAB/Python). For each, calculate the transit frequency_{in}*f*, the frequency at which the magnitude of the transfer function is equal to 1V/V._{T} - The so-called “square-law” model of the FET incorrectly predicts that current becomes arbitrarily small (and
*g*arbitrarily large) as_{m}*V*–_{GS}*V*approaches zero. For values of_{th}*V*smaller than_{GS}*V*(subthreshold operation), the drain current is better described as_{th}

𝐼𝐷 = 𝐼𝑆𝑒𝑉𝐺𝑆/𝑛𝑉𝑇,

where *I _{S}* and

*n*are technology parameters related to the device structure. For

*n*= 1.5, calculate the transconductance efficiency (

*g*/

_{m}*I*) of the FET assuming subthreshold operation. How does it compare to your answers in Part a)?

_{D}Problem 2: Temperature-independent voltage reference (BJT DC analysis)

**Figure 2. PTAT Voltage Generator **

Temperature-insensitive voltage and current references are critical components of precision sensor systems. A temperature-independent reference is created by combining something (e.g. a voltage) that has a positive temperature coefficient (proportional-to-absolute-temperature, PTAT) with something that has a negative temperature coefficient (complementary-to-absolute-temperature, CTAT). When biased with a constant current, the *V _{BE}* of a BJT exhibits a slope of

*approximately*−2mV/C (CTAT). Combining this with the

*difference*of the

*V*’s of two BJT’s biased with different current densities (which is PTAT), properly scaled, will yield a voltage that is (approximately) independent of temperature:

_{BE}𝑉𝐵𝐺 = 𝑉𝐶𝑇𝐴𝑇 + 𝑉𝑃𝑇𝐴𝑇 = 𝑉𝐵𝐸(𝑇) + 𝑀 × ∆𝑉𝐵𝐸(𝑇)

Note that different current densities for *Q _{1}* and

*Q*are achieved by connecting

_{2}*N*transistors in parallel for

*Q*.

_{2}For the following, use the 2N3904 npn transistor (*I _{S}* = 10

^{-14}A, = 300,

*V*= 100) and the UniversalOpamp2 models in Ltspice. Use

_{A}*V*= 5V for the supply voltage.

_{CC}- Determine values for
*N*and*R*such that_{1}*I*=_{C1}*I*= 50A at room temperature (27C)._{C2} - Determine the temperature slope of
*V*via simulation and calculate the value of_{BE1}*M*that would satisfy the above equation. - Verify the design of the PTAT generator in Ltspice, plotting the expression 𝑉
_{𝐵𝐸}(𝑇) + 𝑀 × ∆𝑉_{𝐵𝐸}(𝑇) as a function of temperature. Include your schematic in your submission, showing all relevant voltages and currents at room temperature. Evaluate- the value of
*V*at room temperature, and_{BG} - the maximum deviation from this value over the temperature range −40C to 125C.

- the value of

* *

*Bonus (*: Complete the design of the Brokaw bandgap circuit.

** **Problem 3: Nonlinear distortion in a common-source amplifier

The output voltage of a resistor-loaded common-source amplifier is expressed (neglecting ) as

𝑉𝑜𝑢𝑡 = 𝑉𝐷𝐷 −(𝑉𝑖𝑛 − 𝑉𝑡ℎ)2𝑅𝐷

- (5 points) Assuming the amplifier is driven with a sinusoidal voltage
*V*= a_{in}_{in} sin(2f_{0}t) +*V*, where_{DC}*V*=_{DC}*V*+ 500mV, determine expressions for the_{th}*amplitudes*of the fundamental (sinusoid at f_{0}with amplitude a_{1}) and second harmonic (sinusoid at 2f_{0}with amplitude a_{2}) using the trigonometric relationship

sin^{2}(𝑥) = [1 − cos(2𝑥)]

- Calculate the ratio of a
_{2}/a_{1}for a_{in}= 1mV and a_{in}= 10mV.