Electrical – Given a pull-up network, draw the complimentary pull-down network (CMOS gates)

Consider the circuit diagram in which a CMOS inverter drives a capacitive load.

The delay offered by the inverter is the time taken to charge/discharge the capacitor and is defined as \$\tau = (t_{LH} + t_{HL})/2\$. Where \$t_{LH}\$ is the time required to charge the capacitor. This happens via pMOS transistor and \$t_{LH} = C_{L}R_{p}\$. Similarly, \$t_{HL} = C_{L}R_{n}\$. Where \$R_n\$ and \$R_p\$ are the equivalent resistance of nMOS and pMOS transistors when they are in saturation.

But \$R_p\$ is greater than \$R_n\$ because of the reduced mobility of holes when compared with electrons. Hence low-to-high transition takes more time than high-to-low transition. The width of pMOS is increased so that \$R_p\$ and hence \$t_{LH}\$ and \$\tau\$ can be reduced. Usually pMOS width is made as 2 - 3 times that of nMOS. The most widely used value is 2. Hence making pMOS width 2 times that of nMOS width,

• The propagation delay is reduced as \$t_{LH}\$ is reduced.
• As \$t_{LH} = t_{HL}\$ the voltage transfer curve becomes symmetric and hence the noise margin increases.

This applies for other gates also. Those gates are sized so as to get same current driving capacity as CMOS inverter. This is done by making the resistance equal to that of inverter by changing the width.

Figure shows an inverter along with a two input NAND and NOR. So as to make the resistance of gate equal to that of inverter, the width of series transistors are doubled. The widths of transistors in parallel are not changed since we will be taking critical path for delay calculation.

I think this explains your circuit also.

The answer depends on what you want the "default" configuration to be. For example, say you have a down-stream N-channel MOSFET, and you want it default off. Then you would use a pull-down resistor to ensure this behavior if the input becomes high impedance.

^{simulate this circuit – Schematic created using CircuitLab}

On the other hand, suppose you have an upstream P-channel MOSFET, and want it default off. This time a pull up resistor is required to create this behavior.

^{simulate this circuit}

There's also the alternative case where you want a device to be default-on, in which case the above two cases would be reversed (pull-up for the N-channel MOSFET, pull-down for the P-channel MOSFET).

A few other considerations:

1. I2C lines specify pull-up resistors because devices are "expected" to have an open-drain to ground, and thus need some way to raise the line potential.

2. Analog comparators are usually configured as open-drain devices, and thus also need pull up resistors to get a high potential output.

3. You may draw more current using pullup/pulldown resistors, depending on what's hooked to the input/output.

4. Either configuration could works equally well in your application (i.e. there's no significant advantage one way or the other).

... And any number of very application-specific reasons why one configuration may be preferred.