Common-Source Amplifier

Analog (Integrated) Circuit Design

5 Common-Source Amplifier

Common-Source Amplifier

Figure 25: A MOSFET common-source amplifier with resistive load.

We now want to step up our game, and use more components to design something useful. We will use a basic circuit structure, namely a single-ended common-source amplifier. The structure of this circuit, using a resistor as a load, is shown in Figure 25.

Common-Source Amplifier

\[ A_\mathrm{v} = \frac{V_\mathrm{out}}{V_\mathrm{in}} \approx - \frac{g_\mathrm{m}V_\mathrm{in} R_1}{V_\mathrm{in}} = - g_\mathrm{m}R_1. \]

The function of this circuit is as follows: Assuming the MOSFET \(M_1\) is kept in saturation, then a small-signal voltage \(V_\mathrm{in}\) applied at the gate is converted into a drain current \(I_\mathrm{d}\) by the MOSFET’s transconductance \(g_\mathrm{m}\). Then, this current is converted into a voltage again in the resistor \(R_1\). Ultimately, we have a dc voltage gain \(A_\mathrm{v}\) of

As explained above, it is a good approach to see electronic circuit components as

Common-Source Amplifier

• voltage-to-current converter (MOSFET as common-source or common-gate; resistor),
• current-to-voltage converter (resistor),
• current-to-current converter (MOSFET as common-gate), and
• voltage-to-voltage converter (MOSFET as common-drain)

for better understanding.

5.1 Sense Amplifier Driving 50 Ohm Matched Load

Sense Amplifier Driving 50 Ohm Matched Load

Figure 26: A MOSFET common-source amplifier with 50 Ohm load.

Let us now size and design an exemplary implementation of this amplifier (of course using the \(g_\mathrm{m}/I_\mathrm{D}\) method). In order to have useful real-life specifications, we want to build an amplifier which can be used to sense an on-chip voltage and drive off-chip measurement equipment. Often, this equipment has an input impedance of 50\(\Omega\), and we want to have an impedance-matched output. The voltage gain shall be set to 1 (essentially, we want to sense a voltage and drive the measurement equipment).

The resulting circuit is shown in Figure 26. As the load is usually ground-referred, and we want to avoid a dc-block at the output, we use a PMOS amplifier stage (compare with Figure 25).

Sense Amplifier Driving 50 Ohm Matched Load

Exercise: PMOS-Based Measurement Amplifier

Please think about why exactly we want this measurement amplifier to be based on a PMOS instead of an NMOS.

Sense Amplifier Driving 50 Ohm Matched Load

Important 1: MOSFET Parameters NG and M

When sizing the MOSFET for this example we found that we need a fairly large \(W\), resulting in a MOSFET aspect ratio of \(W/L \gg 1000\). When constructing an integrated circuit out of individual MOSFETs, we strive for an overall IC dimension that is roughly square. For MOSFET with large aspect ratios we need to get them into a comfortable shape.

The power matching requirement at the output mandates that \(R_1 = R_\mathrm{load}\), so \(R'_1 = R_\mathrm{load} \parallel R_1 = 25\,\Omega\). The voltage gain requirement of \(|A_\mathrm{v}| = 1\) results in \(g_\mathrm{m}= 1 / R'_1 = 40\,\text{mS}\).

We now need to find \(W\) and \(L\) of \(M_1\) and calculate the required bias current \(I_\mathrm{D}\). We also need to find the proper \(V_\mathrm{GS}\) to set this current. As usual, we use a Jupyter notebook to calculate these values. Since we require modest speed of this buffer, we use a \(g_\mathrm{m}/I_\mathrm{D}=8\) and set \(L = 0.13\,\mu\text{m}\). The notebook is available here. The resulting circuit including all component values is shown at the end of the notebook (the red input capacitor shows the \(C_\mathrm{gg}\) of the MOSFET).

Sense Amplifier Driving 50 Ohm Matched Load

MOSFET Parameters NG and M

In order to achieve this, we construct the MOSFET out of smaller pieces, and the size of these pieces (called “gate fingers”) is controlled by the parameter ng. These MOSFET gate fingers all have the same \(L\), but their width is \(W_\mathrm{finger} = W / \text{ng}\). All these individual smaller MOSFETs are connected in parallel.

In order to increase the MOSFET model accuracy, often the maximum value of \(W_\mathrm{finger}\) is limited. In the case of SG13G2 \(W_\mathrm{finger} \le 10\,\mu\text{m}\).

Sense Amplifier Driving 50 Ohm Matched Load

MOSFET Parameters NG and M

In order to construct even larger MOSFETs, we can connect multiple MOSFETs in parallel. We can do this in the circuit editor by placing and connecting these MOSFETs; but since this is often used there is a more convenient way: By using the parameter m (“multiplier” or “multiplicity”) we instantiate \(m\) MOSFETs connected in parallel.

Sense Amplifier Driving 50 Ohm Matched Load

MOSFET Parameters NG and M

When to use ng and when to use m? The use of ng results in a more compact IC layout, and is thus generally preferable. Only in certain instances (e.g., when using a really large \(W\)) m should be used. Further, the thoughtful use of ng allows one to construct all the NMOS and PMOS of a circuit out of the same gate finger elements. This will result in a very compact layout!

Sense Amplifier Driving 50 Ohm Matched Load

Exercise: Measurement Amplifier Simulation

Please go through the sizing notebook of the measurement amplifier and double-check the calculations. Do you agree that the calculations are correct?

Once you agree with the circuit sizing please build an Xschem simulation testbench where you simulate the small-signal voltage gain \(A_\mathrm{v}\) of this measurement amplifier if it is driven with an ideal voltage source. Keep in mind that the maximum MOSFET finger width is 10µm in this technology, so you need to set the parameter ng accordingly (see Important 1).

Sense Amplifier Driving 50 Ohm Matched Load

Exercise: Measurement Amplifier Simulation

• What is the dc gain of this amplifier when loaded with 50\(\Omega\)?
• The dc gain is likely not exactly 0 dB. Why is this so?
• Increase the width \(W\) of the PMOS until the gain is correct. What is the \(W\) that you had to set, and how much is \(I_\mathrm{D}\) now?
• What is the bandwidth (i.e., the -3 dB corner frequency) of the output voltage, when the voltage source has a source resistance of 1k\(\Omega\)?

Sense Amplifier Driving 50 Ohm Matched Load

Exercise: Measurement Amplifier Simulation

If you get stuck, here is the solution to this exercise, and it is also shown in Figure 27.

Sense Amplifier Driving 50 Ohm Matched Load

Exercise: Measurement Amplifier Simulation

Figure 27: Simulation schematic of the common-source measurement amplifier.

Sense Amplifier Driving 50 Ohm Matched Load

By now we have designed a measurement amplifier based on a common-source stage. One problem with this stage is the relatively large input capacitance \(C_\mathrm{GG}\) of approx. 0.35pF, which loads the input source. Another even more severe issue is that the bias point in this circuit is set by the dc voltage level at the input. In general, we want a setup where the bias points of the circuit are largely independent of the dc input voltages. This is why in integrated circuit design we often design differential circuits where the input and output signals are given by the differential voltages, and are largely independent from the common-mode voltages. This is usually an advantage.