Question E6C07:
What best describes a pull-up or pull-down resistor?  

Choices:  
A: A resistor in a keying circuit used to reduce key clicks  
B: A resistor connected to the positive or negative supply used to establish a voltage when an input or output is an open circuit  
C: A resistor that ensures that an oscillator frequency does not drift  
D: A resistor connected to an op-amp output that prevents signals from exceeding the power supply voltage    

Correct Answer is  B: A resistor connected to the positive or negative supply used to establish a voltage when an input or output is an open circuit  

Correct answer: B

Why B is correct
- A pull-up connects the node to the positive supply through a resistor; a pull-down connects to ground through a resistor. This establishes a defined logic level when the input/output is otherwise floating (open circuit).
- Common uses:
  - Digital inputs with a switch: when the switch is open, the pull-up makes the input a valid logic HIGH; when closed to ground, it becomes LOW.
  - Open-collector/open-drain outputs: the pull-up provides the HIGH level when the transistor is off.

Why the other choices are incorrect
- A: “Reduce key clicks” refers to shaping RF or audio keying waveforms (e.g., rise/fall time shaping). That’s not what pull-ups/pull-downs do.
- C: Oscillator drift is addressed by temperature compensation, crystal ovens, or varactors—not by pull-up/pull-down resistors.
- D: Preventing op-amp outputs from exceeding supply rails is done with clamping diodes, rail-to-rail parts, or supply limits. A pull-up/down on an op-amp output won’t enforce rail limits.

Useful formulas and rules of thumb
- Define node voltage against leakage current:
  - For a pull-up with leakage current $I_{\text{leak}}$ flowing out of the node:
    $$V_{\text{node}} \approx V_{CC} - I_{\text{leak}} R_{\text{pull-up}}$$
  - For a pull-down with leakage current flowing into the node:
    $$V_{\text{node}} \approx I_{\text{leak}} R_{\text{pull-down}}$$
- When a switch closes to ground with a pull-up:
  - Low-level current when asserted: $$I_{\text{low}} = \frac{V_{CC}}{R_{\text{pull-up}}}$$
  - Choose $R$ so $I_{\text{low}}$ is within device limits and not wasteful.
- Rise/fall time with input capacitance $C_{\text{in}}$:
  $$\tau = R_{\text{pull}} \, C_{\text{in}}$$
  Smaller $R$ speeds edges but increases current when active.
- Typical values:
  - CMOS logic: $10\ \text{k}\Omega$ is common; range $4.7\ \text{k}\Omega$ to $100\ \text{k}\Omega$ depending on speed/noise.
  - Open-drain drivers: pick $R$ to meet both rise-time needs and sink-current ratings. Example: with $V_{CC}=5\ \text{V}$ and $R=10\ \text{k}\Omega$, the sink current is $0.5\ \text{mA}$ and $\tau = 10\ \text{k}\Omega \cdot 20\ \text{pF} = 200\ \text{ns}$ for a small load.