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An op-amp circuit with two inverting amplifiers in cascade is shown with a variable resistance Rx. The input voltage is VSRC and input current is lin. Using node voltage analysis, derive an expression for the voltage gain Vout/VSRC as a function of resistor Rx. What is the voltage gain when Rx is infinite? What is the voltage gain when Rx is zero? Can you now figure out why Rx is used?

An op-amp circuit with two inverting amplifiers in cascade is shown with a variable resistance Rx. The input voltage is VSRC and input current is lin. Using node voltage analysis, derive an expression for the voltage gain Vout/VSRC as a function of resistor Rx. What is the voltage gain when Rx is infinite? What is the voltage gain when Rx is zero? Can you now figure out why Rx is used?

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An op-amp circuit with two inverting amplifiers in cascade is shown with a variable resistance R x . The input voltage is V SRC and input current is lin. Using node voltage analysis, defिve an expression for the voltage gain V out / V SRC as a function of resistor R x . What is the voltage gain when R x is infinite? What is the voltage gain when R x is zero? Can you now figure out why R x is used?

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An NMOS amplifier is shown in Figure 1. Transistor M1 is biased in the saturation region for an amplifier application. The circuit is biased with a resistive voltage divider consisting of R1 and R2, a source degeneration resistor RS, and a load resistor RD. The drain bias current for the design is ID = 500 μA and VDS is 1.625 V. The device parameters are: L = 0.5 μm, W = 10 μm, kn’ = 200 μA/V2, Vtn = 0.5 V, and λn = 0. analyze the frequency response of the amplifier. a) Draw a midband small signal ac equivalent circuit model for the amplifier. For midband you can assume the reactance of Cin is sufficiently low that it is a short circuit. b) Derive an expression for the midband voltage gain transfer function Vout /Vsig. The amplified output signal is taken from the drain terminal and Vout = Vd. Write your gain function in terms of variables only. c) Evaluate the midband gain and calculate a value both in V/V and dB. d) Analyze the frequency response of the input network including the capacitor Cin. Find an expression for the transfer function H1(jω) = Vg/Vsig. e) Evaluate H1(jω) = Vg/Vsig and make a Bode plot of the magnitude of H1(jω). The x-axis is ω (log scale) and the y-axis is the magnitude in dB. f) Use the LTSPICE circuit template and verify the frequency response of the amplifier circuit. Include a copy of the schematic and the frequency response plot. Use 20 points per decade and a frequency span of 0.1 Hz to 100 Hz.
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In this question, you are asked to find the effective transconductance (Gm) and the resistance into the drain (Rx) of a common-source amplifier with source degeneration. Based on the results, the voltage gain of a common-source amplifier with source degeneration will be evaluated a) The figures shown below are a circuit to find the effective transconductance (G) of the NMOSEFT with source degeneration (left) and its corresponding small-signal circuit (right). It is noted that the output is shorted to VDD (ac grounded) since the definition of effective transconductance is the ratio between the short-circuit output current and the input signal voltage. Prove that Gm is given by Gm = id/vin = gm/1+gmRs In this calculation, the current passing through ro can be neglected since, in general, ro is very large when the NMOSFET operates in saturation region and so this current is very small. Thus, the indication of id is the current of the voltage-controlled current source (gmvgs) only. b) The figure shown below is the method to evaluate the resistance looking into the drain (i.e. Rx) of a source-degenerated NMOSFET. The circuit is shown on the left while the equivalent small-signal modeling is shown on the right. It is noted that the bias condition (VBiAS) is set so that the values of gm and ro, can be defined. Moreover, there is no input signal (i.e. Vin = 0) since we would like to see the value of Rx which is due to the circuit only but not due to the external effect. Based on the above small-signal model, prove that RX = ro(1 + gmRS) The complete common-source amplifier with source degeneration is shown below. c) The complete common-source amplifier with source degeneration is shown below. Prove that the voltage gain of this amplifier is given by v. Vin Explain the reason(s) why the voltage gain is negative. What is the physical meaning of negative voltage gain?

In this question, you are asked to find the effective transconductance (Gm) and the resistance into the drain (Rx) of a common-source amplifier with source degeneration. Based on the results, the voltage gain of a common-source amplifier with source degeneration will be evaluated a) The figures shown below are a circuit to find the effective transconductance (G) of the NMOSEFT with source degeneration (left) and its corresponding small-signal circuit (right). It is noted that the output is shorted to VDD (ac grounded) since the definition of effective transconductance is the ratio between the short-circuit output current and the input signal voltage. Prove that Gm is given by Gm = id/vin = gm/1+gmRs In this calculation, the current passing through ro can be neglected since, in general, ro is very large when the NMOSFET operates in saturation region and so this current is very small. Thus, the indication of id is the current of the voltage-controlled current source (gmvgs) only. b) The figure shown below is the method to evaluate the resistance looking into the drain (i.e. Rx) of a source-degenerated NMOSFET. The circuit is shown on the left while the equivalent small-signal modeling is shown on the right. It is noted that the bias condition (VBiAS) is set so that the values of gm and ro, can be defined. Moreover, there is no input signal (i.e. Vin = 0) since we would like to see the value of Rx which is due to the circuit only but not due to the external effect. Based on the above small-signal model, prove that RX = ro(1 + gmRS) The complete common-source amplifier with source degeneration is shown below. c) The complete common-source amplifier with source degeneration is shown below. Prove that the voltage gain of this amplifier is given by v. Vin Explain the reason(s) why the voltage gain is negative. What is the physical meaning of negative voltage gain?

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Consider the circuit shown, which is a model of an amplifier. The input voltage is vs and the output voltage is vo. The resistance ro, has value 100K, which means 100 kiloohm (note the strange spelling) or 100 x 10^3 ohm. The value of the resistor r_pi is 2.5K (2.5 X 10^3 ohm). The controlled current source has transconductance gm = 0.04 S. This means that if the voltage across r_pi is v_pi, the current source has magnitude gmr_pi. Something that often confuses newcomers to electronics is the ground symbol: In the diagram, this symbol appears 4 times. All the grounds are connected and are, in fact, the same node. Using the information provided, find an expression for the ratio Av = vo/vs, which is called the voltage gain of the amplifier.
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