View source for Design: A Simple Common-Source Amplifier

* '''Instructions''': This activity is structured as a tutorial with an activity at the end. Should you have any questions, clarifications, or issues, please contact your instructor as soon as possible. 
* At the end of this activity, the student should be able to:
# Design a simple common-source amplifier.

== Activity 1: Transistor Intrinsic Gain ==

We can determine the intrinsic NMOS small-signal gain, <math>a_0 = g_m \cdot r_o</math>, for a desired DC operating point, i.e for a given drain current, <math>I_{DC}</math>, and drain-to-source voltage, <math>V_{DS}</math>. This implies a certain gate-to-source voltage, <math>V_{GS}</math>. For square-law devices, we can easily calculate the required <math>V_{GS}</math> that corresponds to <math>I_{DC}</math> and <math>V_{DS}</math>. However, for deep submicron devices that do not follow the square law, we can either run simulations to determine this <math>V_{GS}</math>, or instead, we can let SPICE calculate <math>V_{GS}</math> for us. As seen in Fig. 1, we can use negative feedback to obtain the appropriate <math>V_{GS}</math>.

{|
| [[File:Nmos-gain-sim-setup.png|thumb|225px|Figure 1: The NMOS intrinsic gain simulation setup.]]
| [[File:Nmos-1v8-lvt-gain.png|thumb|400px|Figure 2: The NMOS intrinsic gain.]]
|-
|}

Using the circuit in Fig. 1, with <math>W=40\mathrm{\mu m}</math>, <math>L=0.15\mathrm{\mu m}</math>, <math>I_D=1\mathrm{mA}</math>, and the ideal amplifier gain, <math>A_v=1000</math>:
* Sweep <math>V_{DS}</math> from 200mV to 1.8V, and plot <math>V_{GS}</math> as a function of <math>V_{DS}</math>. 
* From the <math>V_{GS}</math> vs. <math>V_{DS}</math> plot, derive the NMOS instrinsic gain, <math>a_0 = \left(\frac{\partial V_{GS}}{\partial V_{DS}}\right)^{-1}</math>, as a function of <math>V_{DS}</math>.
* Repeat for transistor lengths of <math>0.20\mathrm{\mu m}</math>, <math>0.25\mathrm{\mu m}</math>, <math>0.30\mathrm{\mu m}</math>, <math>0.35\mathrm{\mu m}</math>, and <math>0.40\mathrm{\mu m}</math>, and generate the graphs in Fig. 2.

You can use a voltage-controlled voltage source (VCVS) to model the ideal amplifier. Aside from obtaining the intrinsic gain at different lengths, we can use this circuit as a replica bias generator, to generate the DC input voltage of a common-source amplifier using the same transistor, as shown in Fig. 3.

== Design: A Common-Source Amplifier ==
Now that we have obtained the transistor (1) large-signal characteristics, i.e. the transfer and output characteristics, (2) the small-signal parameters, <math>g_m</math>, <math>r_o</math>, <math>f_T</math>, and <math>a_0</math>, and (3) the figures of merit, <math>V^* =V_{ov}=\frac{2I_D}{g_m}</math> and <math>f_T\cdot \frac{g_m}{I_D}</math>, we can now put everything together and design a simple amplifier.

=== Part 1 ===
You are tasked to design a simple common-source amplifier biased with an ideal current source, with the following specifications:
* Small-signal low-frequency voltage gain: <math>\left|A_v\right| = \left|\frac{v_{out}}{v_{in}}\right| > 40</math> for an output DC voltage of <math>\frac{V_{DD}}{2} = 0.9\mathrm{V}</math>, and an output swing of at least <math>400\mathrm{mV}</math> (<math>\pm 200\mathrm{mV}</math> around <math>0.9\mathrm{V}</math>)
* Unity-gain frequency: <math>f_u = 100\mathrm{MHz}</math> for a load capacitance <math>C_L=5pF</math>
* <math>V^*=200\mathrm{mV}</math>

{|
| [[File:Cs-amp-gain-sim-setup.png|thumb|500px|Figure 3: A simple NMOS common-source amplifier, where the output voltage, <math>v_{out}</math>, is the voltage across the load capacitor, <math>C_L</math>.]]
|-
|}

You are to submit:
* A short description of the design procedure you used to obtain <math>I_D</math>, <math>W</math>, and <math>L</math>.
* Any calculations you have done. 
* A DC sweep of <math>v_{out}</math> vs. <math>v_{in}</math>.
** What is the maximum symmetric output voltage swing for <math>\left|A_v\right| > 40</math>?
** What is the corresponding input voltage swing?
* A plot of the magnitude response showing the low frequency gain, and the unity-gain frequency.
* Are these your expected results?

=== Part 2 ===
You now wish to test the technology and design an amplifier has the highest unity-gain frequency, <math>f_T</math>, you can get, while maintaining the voltage gain, <math>\left|A_v\right| > 40</math>, for an output swing of at least <math>400\mathrm{mV}</math>, <math>C_L=5pF</math>, and an output DC voltage of <math>0.9\mathrm{V}</math>.

You are to submit:
* A short description of the design procedure you used to obtain <math>V^*</math>, <math>I_D</math>, <math>W</math>, and <math>L</math>.
* Any calculations you have done. 
* A DC sweep of <math>v_{out}</math> vs. <math>v_{in}</math>.
** What is the maximum symmetric output voltage swing for <math>\left|A_v\right| > 40</math>?
** What is the corresponding input voltage swing?
* A plot of the magnitude response showing the low frequency gain, and the unity-gain frequency.
** What is the maximum <math>f_T</math> you achieved?
** How much more current are you consuming compared to the amplifier in Part 1?

=== Part 3 ===
You are now asked to design an amplifier with the lowest DC power consumption, <math>P_{DC}=V_{DD}\cdot I_D</math>, you can achieve, while maintaining the voltage gain, <math>\left|A_v\right| > 40</math>, for an output swing of at least <math>400\mathrm{mV}</math>, <math>C_L=5pF</math>, and an output DC voltage of <math>0.9\mathrm{V}</math>.

You are to submit:
* A short description of the design procedure you used to obtain <math>V^*</math>, <math>I_D</math>, <math>W</math>, and <math>L</math>.
* Any calculations you have done. 
* A DC sweep of <math>v_{out}</math> vs. <math>v_{in}</math>.
** What is the maximum symmetric output voltage swing for <math>\left|A_v\right| > 40</math>?
** What is the corresponding input voltage swing?
* A plot of the magnitude response showing the low frequency gain, and the unity-gain frequency.
** What is the maximum unity-gain frequency you achieved?
** How much more current are you consuming compared to the amplifier in Parts 1 and 2?

== Report Guide ==
Write up a report (maximum of 6 pages including figures) answering the questions above. Include annotated graphs if needed.

== Submission ==
This activity is for both graduate and undergraduate students. For UP students, the submission bin link will be posted in Piazza.