<aside> 💡 Rule of Thumb for Voltage Source Placement: I feel like placement voltage source if for purpose of driving a charge into it, is just asking the question of if the two endpoint nodes you specified goes through a circuit or component you wanted to have sent through. Motivation would be to test the input or output of a circuit (like in our example) or to simulate the behavior.

The placement of a voltage source depends on what you're trying to simulate. Here are some general guidelines:

1. Stimulus Sources: If you're trying to provide an input to the circuit, place the voltage source in such a way that it effectively drives the input nodes.
2. Power Supply: If the voltage source is meant to be a power supply, then it's usually connected between the supply node and ground.
3. Signal Measurement: If you're using a voltage source to measure a parameter (like in small-signal analysis), it would be inserted in the circuit where you want the measurement to occur.
4. Ground Reference: It's common to have one terminal of the voltage source connected to ground when the source is used for stimulus or measurement, as this provides a reference voltage level.

voltage sources like Vin vin 0 pulse(3.3,0,5ns,.1ns,.1ns,4.8ns) are idealized constructs that force a voltage difference between two nodes—in this case, between the node vin and ground (notated as 0). The directive doesn't necessarily specify a "flow" of current; rather, it sets up a voltage difference that will induce a current flow based on the rest of the circuit.

In the Context of the SPICE Simulation: maintain a specified voltage difference between its terminals. Current only flows when the transistors gates turn on, effectively opening the channel to allow electrons or charge to flow through </aside>

A: 814.80uA

Effective resistence = (1.2V - 0V) / (814.8uA - 0V) = 1472.7540500736 ohm (Ω)

effective channel sheet resistance:

1472.7540500736 ohm (Ω) * 2 = 2945.50810015 ohm

B:

VGS=0V and VDS=2.5V: 5.155pA

What is capacitance, intuitively?

Capacitance is essentially the ability of a system to store electrical charge. Imagine a parallel-plate capacitor as two large, flat "buckets" facing each other. The bigger the buckets (plates), the more water (charge) they can hold. Also, the closer the buckets are to each other, the more water they can hold due to mutual influence. That's analogous to increasing the surface area of the plates or decreasing the distance between them to increase capacitance. In essence, a capacitor "holds" electric charge in an electric field between its plates, and its ability to do so is quantified as capacitance.

Why do we need to refresh the capacitors' charge?

In digital circuits, particularly in memory elements like DRAM (Dynamic Random-Access Memory), the capacitors store bits of information as charge. Over time, due to leakage currents and other factors, the charge in these capacitors starts to dissipate. If the charge level drops below a certain threshold, the information stored could be lost or misread. Therefore, it is necessary to periodically "refresh" the charge in these capacitors to maintain data integrity.