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Draw the differential-mode half-circuit equivalent assuming the two current sources are ideal and both sides are fully identical and symmetrical. Derive an expression for the effective transconductance (Gm) of the circuit in (1) in the s-domain. What is the Gm at DC (ω = 0) ? Based on (2), calculate the zero and the pole frequency and sketch the effective transconductance (Gm) vs. ω. Assuming the output pole at 1 /RDCL is the dominant pole, determine the product of RSCS to achieve "pole-zero" cancellation. Based on this pole-zero cancellation determined in (4), sketch the gain response |Av| vs. ω, assuming ro = ∞.

Draw the differential-mode half-circuit equivalent assuming the two current sources are ideal and both sides are fully identical and symmetrical. Derive an expression for the effective transconductance (Gm) of the circuit in (1) in the s-domain. What is the Gm at DC (ω = 0) ? Based on (2), calculate the zero and the pole frequency and sketch the effective transconductance (Gm) vs. ω. Assuming the output pole at 1 /RDCL is the dominant pole, determine the product of RSCS to achieve "pole-zero" cancellation. Based on this pole-zero cancellation determined in (4), sketch the gain response |Av| vs. ω, assuming ro = ∞.

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  1. Draw the differential-mode half-circuit equivalent assuming the two current sources are ideal and both sides are fully identical and symmetrical.
  2. Derive an expression for the effective transconductance ( G m ) of the circuit in (1) in the s-domain. What is the Gm at DC ( ω = 0 ) ?
  3. Based on (2), calculate the zero and the pole frequency and sketch the effective transconductance (Gm) vs. ω .
  4. Assuming the output pole at 1 / R D C L is the dominant pole, determine the product of RSCS to achieve "pole-zero" cancellation.
  5. Based on this pole-zero cancellation determined in (4), sketch the gain response | A v | vs. ω , assuming ro = ∞ .

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In the circuit shown in Fig. 3, assume that transistors M1 A and M1 B are perfectly matched and that ro = ∞. The elements labeled Ix are ideal DC current sources. (a) Assume the two transistors are biased in the saturation region that the VGS of the transistors is known. Find expressions, in terms of component values and relevant transistor parameters, for the dc voltages and dc currents at the drain, gate, and source transistor terminals. (b) Draw the the differential-mode half-circuit small-signal schematic for this circuit. Then find the differential-mode gain Adm. (c) Draw the the common-mode half-circuit small-signal schematic for this circuit. Then find the common-mode gain Acm. Figure 3

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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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a. For the circuit shown below, show a clean and labeled small signal equivalent circuit and derive the expression for vo/vb, (vb is the small signal voltage at the base node) vo/vsig, Rin and Rout. (b) This is the design part. The specifications are as follows: The required gain vo/vb = −120 V/V, Ic = 1 mA. and the require voltage swing at the output is ±3 V around the DC value of the output. (Hint: Do not use the generic design rule. You should be able to find the DC voltages at the collector and emitter from the specifications). Assume Vcc = 8 V. For this design assume VA = ∞ (this makes ro = ∞), V T (Thermal Voltage) = 25 mV, VBE = 0.7 V, VCEsat = 0.3 V and β = ∞. Find the values of RC, RE, RB1, and RB2. (c) If the β = 100 instead of the design value, find the new Ic. Now assuming VA = 50 V find vo/vsig, Rout and RIN. For this part assume Rsig = 10 kΩ. Punt: If you could not answer (b), use RC = 3 kΩ, RE = 2 kΩ, RB1 = 50 kΩ, and RG2 = 30 kΩ (d) Run a transient simulation of the designed circuit in Multisim. Use the same BJT used in the lab simulation. Show the input voltage v sig and output voltage v o on the same plot. Choose vsig to be at 1 kHz and 10 mV peak sinusoidal. Compare with calculated value of the gain in part c.
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