34.1.6. Finding Drain Resistance

In this section, we start by setting a target current, say I = 0.5 mA, and using the I-V characteristic curve equation: I_DS = K * W * (V_GS - V_th)^2, while ignoring the channel length modulation term for simplification.

The process begins by choosing the desired drain current (0.5 mA in our example). We use the MOSFET I-V equation to find the gate-source voltage (V_GS) that will yield this current. By substituting our values into the equation, we simplify it by neglecting the channel length modulation, which allows us to focus on the essential relationship between current and voltage. This results in a focus on determining how to configure the circuit to achieve the desired performance.

Think of setting a target running speed during a training session. By deciding on a pace (the current), you can adjust your stride (the voltage) accordingly, only considering the essentials like form and stamina while ignoring minor factors that might affect your performance in the short term, such as weather conditions.

From the equation, we find (V_GS - V_th) = 1 V, meaning V_GS = V_th + 1 V. If V_th is known to be 1 V, then V_GS must be 2 V.

Here, we solve for V_GS using the value obtained from the equation. By knowing the threshold voltage (V_th), we can determine how much overdrive voltage (the excess above V_th) is needed to achieve our target current. The resulting V_GS is crucial for ensuring that the MOSFET operates in saturation, which is necessary for our amplifier to function properly.

When cooking, each ingredient has an optimal quantity to produce the best dish. Similarly, V_GS must exceed V_th to ensure the MOSFET operates correctly, just like using the right amount of spices enhances the flavor of the meal.

To achieve the desired V_GS from a 12 V supply, we set up the relation V_GS = V_dd * R2 / (R1 + R2), leading us to define the ratio of resistors: R1 = 5 * R2.

We manipulate the voltage divider formula to relate the resistors R1 and R2 that generate our required V_GS. This leads to the conclusion that R1 must be five times R2, which will help us maintain the proportion needed for proper operation of the amplifier.

Imagine a seesaw where the balance depends on the relative weights on either side. If one side needs to be heavier (R1) to balance the lighter side (R2), we can adjust the weights to find the right balance for the seesaw to function properly.

Given that R1 + R2 totals 240 kΩ, and the ratio allows us to conclude R2 = 40 kΩ, R1 = 200 kΩ. Thus, we arrive at specific resistor values necessary for our circuit design.

Using the previous relation and our total resistance equation, we solve to find the specific values of R1 and R2 that will achieve our target gate-source voltage. These fixed values will ensure that the biasing conditions are satisfied for the desired amplifier performance.

If you're baking cookies and the recipe asks for a total of 240 grams of ingredients (R1 + R2), with one ingredient needing to be five times the amount of another (R1 = 5 * R2), you can figure out the specific amounts needed for each after a little math, ensuring your cookies turn out just right.

To maximize the output swing, we center the target voltage for V_D, setting it midway between V_dd and V_GS - V_th. This gives us R_D = (V_dd - (V_GS - V_th)) / (2 * I_DS).

To ensure that our amplifier can output the largest possible voltage swing without distortion, we calculate the drain resistance (R_D) by positioning the DC operating point at a sweet spot—approximately halfway between the supply voltage and the minimum drain voltage. This ensures ample room for signal fluctuations around the DC point.

Think of a swing at a playground; positioning the swing at the right height allows for the greatest range of motion (swing) before hitting the ground. If it’s too high or too low, the potential for fun (signal swing) reduces significantly.

Finally, the design results in output swing, gain, and resistances: the output swing is ±5.5V, gain is determined using the relationship g_m * R_D, and we also calculate input and output resistances.

In this segment, we perform a final evaluation of the circuit’s performance based on the calculated values for output swing, voltage gain, input and output resistances. This evaluation confirms whether our circuit design meets the intended specifications and functionality.

After building a model airplane, you wouldn't just leave it in the box; you’d want to fly it! Testing its performance helps you see if it flies as expected, just like evaluating an amplifier's output swing and gain confirms that it functions correctly in its intended application.

--