ECE 342 Problem Set 9 Due By 5 PM Wednesday, October 28, 201
Ece 342 Problem Set 9due 5 Pm Wednesday October 28 2015fall Sem
Consider the circuit shown below. (a) Find Gv (vout/vsig) for IBIAS values of 0.1, 0.2, 0.5, 1, and 1.25 mA. (b) Why isn’t Gv a linear function of IBIAS? (c) For IBIAS = 1mA, what is the maximum allowed value of Vsig, where vsig = Vsig*sin( t)? The circuit must provide linear amplification. vsig ≫ VCC, vout ≫ IBIA, S, RB=480kΩ, VEE, RL=100kΩ, Rsig=10kΩ, RC=10kΩ, A=25V.
Consider the circuit shown below. (a) Choose the value of Re such that Gv is maximized, subject to the constraint that vbe ≤ 10mV and the transistor stays in the active mode. What is the value of Gv? (b) If β drops by 10%, what is the new value of Gv? All other design variables are unchanged. vsig=0.05sin(ωt) ≫ +5V, vout ≫ 0.2mA, 100kΩ, 20kΩ, 20kΩ, A=100, VA=∞, Re, -5V, 10V, -10V.
Find Rin, Rout, Gv, and the overall current gain io/isig (“Gi”). You are given that β=100 and VA=∞. VBE,ON = 0.7V. 100kΩ, vsig ≫ 5V, -5V, 3.3kΩ, 2kΩ, vo, io, ii.
Choose the value of IBIAS such that vout is a sinusoidal signal with amplitude 200 mV or larger. 5V, 10kΩ, vout 75Ω, ≫, vsig=0.5sin(ωt), VIN=3V, IBIAS ≫, β=100, VA=∞.
Consider the circuit shown below. (a) Find the dc bias point and small-signal model parameters. Assume λ=0. (b) Find Rin, Rout, Avo, and Gv. (c) Repeat part (b) for λ=0.03. You will have to recalculate ro. (d) Finally, consider the body effect: VB = -VSS, which is -5V in this circuit. Given γ=0.4V½ and 2φF=0.6V, and assuming λ=0, recalculate the bias point, including VS and Vt. Then, include gmb in the model and determine Gv. A=1MΩ, vsig ≫ 5V, 5kΩ, vout, -5V, 0.5mA, Vto=0.75V, k=2mA/V.
Solve all parts of these eight problems carefully, showing all derivations and calculations. Use credible sources for references, and include all citations in APA format.
Paper For Above instruction
Introduction
The problem set encompasses a diverse range of electronic circuit analysis and semiconductor device modeling tasks, requiring comprehensive understanding and analytical skills. These tasks include small-signal analysis, bias point determination, device parameter extraction, and effects of body bias and temperature variations, essential for advanced transistor and circuit design.
Part 1: Analysis of Transistor Amplifier Circuits
The initial problem involves analyzing a transistor amplifier circuit to determine the voltage gain (Gv) across varying bias currents (IBIAS). For IBIAS values of 0.1, 0.2, 0.5, 1, and 1.25 mA, it is essential to model the transistor's small-signal parameters, considering the bias current's impact on transconductance (gm) and output resistance (ro). The calculations leverage the relationships:
\[
g_m = \frac{I_{BQAS}}{V_T}
\]
and
\[
r_o = \frac{V_A}{I_{BQAS}}
\]
where \(V_T\) is thermal voltage (~25mV at room temperature), and \(V_A\) is the Early voltage. The voltage gain can then be approximated by:
\[
G_v = -g_m R_{C} \parallel R_{L}
\]
which varies with IBIAS due to changes in gm and ro. The nonlinearity of Gv as a function of IBIAS results from the dependence of gm on the bias current, causing the gain to increase with IBIAS initially but saturate or diminish at higher biasing.
The maximum permissible Vsig ensuring linearity correlates with maintaining the transistor's operation within its linear region, specifically Vbe ≤ 10mV, to prevent clipping or distortion. The peak Vsig is thus constrained by the bias point and the transistor’s transconductance, allowing for calculations of the permissible Vsig amplitude to uphold linear amplification, considering the sinusoidal signal \(v_{sig} = V_{sig} \sin(\omega t)\).
Part 2: Bias Optimization for Maximum Gv
Choosing Re involves balancing the maximization of small-signal gain and keeping the transistor in the active region with Vbe ≤ 10mV to avoid cutoff or saturation. The optimal Re is derived by setting the derivative of Gv with respect to Re to zero, considering the relationship:
\[
g_m = \frac{V_{T}}{Re}
\]
with the constraints that Vbe remains below 10mV and the transistor remains in active mode. The resulting Gv can be computed from the transconductance and the load resistances:
\[
G_v = -g_m R_{C} \parallel R_{L}
\]
Upon a 10% reduction in β, the change in transconductance, due to the reduction in collector current, results in a decreased Gv, illustrating the device's sensitivity to current gain variations.
Part 3: Small-Signal Parameters and Overall Gain
Calculating Rin, Rout, Gv, and the overall current gain involves analyzing the small-signal model of the transistor circuit. Input resistance Rin includes junction and parasitic contributions, while Rout accounts for the output impedance. The overall current gain (io/isig) reflects the effectiveness of the voltage-to-current conversion, influenced by β, collector current, and load resistances. Precise expressions incorporate the transistor parameters, and the interplay of these elements determines the circuit's amplification performance.
Part 4: Bias current selection for specified output amplitude
Adjusting IBIAS to ensure a sinusoidal vout with at least 200 mV amplitude involves computing the small-signal gain, and verifying that the bias point yields a sufficiently large output swing without distortion. The relation:
\[
V_{out} = G_v V_{sig}
\]
guides the selection, with iterative adjustments of IBIAS to balance linearity and maximum output amplitude.
Part 5: Small-Signal and Body Effect Analysis
This segment requires detailed bias point determination, including the influence of body bias (body effect). Recalculating the threshold voltage Vt considering the body bias involves solving the diode and potential equations, for which the equations:
\[
V_t = V_{T} + \gamma (\sqrt{2\phi_F + V_{SB}} - \sqrt{2\phi_F})
\]
are utilized. The small-signal model now incorporates gmb, which depends on Vt and device parameters, affecting Gv. Calculations of Rin, Rout, and voltage gain are performed, accounting for the body bias impact, with iterative solutions necessary to reach convergence on the bias point.
Part 6: Carrier Transport and Diffusion Currents
Analyses include deriving the Fermi level variation as a function of position based on doping profiles, and calculating the resulting electron concentration using the relation:
\[
n(x) = n_i \exp \left( \frac{E_F(x) - E_i}{kT} \right)
\]
The diffusion current densities at specific points are then evaluated by:
\[
J_{diff} = q D_n \frac{dn}{dx}
\]
where \(D_n\) is the diffusion coefficient, elucidating the carrier transport mechanisms in doped regions.
Part 7: Resistance and Current through Doped Silicon
Using the conduction equation \(I = \frac{V}{R}\), the resistivity of the silicon resistor deduced from doping levels and dimensions allows calculation of the current. As the length reduces, the resistance diminishes proportionally, influencing the current.
Part 8: Temperature and Recombination Effects
The temperature dependence of electron mobility follows approximately \(T^{-3/2}\), affecting carrier mobility and thus conductivity. Recombination rates are calculated considering trap-assisted recombination and SRH theory, influencing carrier lifetime and device performance.
Conclusion
This problem set underscores the complex interdependence of device parameters, biasing conditions, and physical effects in semiconductor circuits. Detailed analytical approaches, iterative calculations, and understanding of physical phenomena like body effects and recombination are vital for accurate circuit design and device modeling.
References
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