Electronics & Circuits · Study deck
DAC and PWM: Output Foundations
A digital pin cannot produce every analog voltage on its own.
Voltage Vera is your guide for this deck.
After studying this chapter
Learning objectives
You will be able to:
- Explain DAC Operation: Describe how digital-to-analog converters translate binary values into proportional voltages
- Apply DAC Formulas: Calculate output voltage from digital input using the DAC transfer equation
- Implement PWM Output: Generate pulse width modulation signals as pseudo-analog output for actuator control
- Design RC Filters: Compute component values for low-pass filters that convert PWM to smooth analog voltage
Major section
Start Simple
The computer holds a number, but the lamp needs voltage, current, and safe timing.
- The path between them decides whether the physical result matches the command.
- An analog-to-digital converter means a circuit that turns a voltage into a number; it is called an ADC.
- Modulation means changing a signal to carry or control information.
Major section
Start Simple (continued)
A digital-to-analog converter (DAC) means a circuit that turns a number into a voltage or current.
- Pulse-width modulation means control made by changing how long a signal stays on; it is called PWM.
- An actuator means a part that creates a physical action.
- This runway does not size a driver or prove smooth motion.
Major section
Phoebe's Field Notes: Why PWM Can Behave Like a DAC
The mathematical gist.: An 8-bit endpoint DAC on 5 V has step $q=5/255=19.6$ mV and code 153 gives 3.00 V.
- PWM instead gives $V_{avg}=DV_{high}$.
Major section
Digital-to-Analog Converters (DAC)
The drawing communicates dAC conversion contract from bounded digital code through reference and transfer function to measured analog output.
- For digital-to-analog converters (dac), these labels identify the boundary where an assumption must become a calculation or measurement.
Major section
Putting Numbers to It
For an 8-bit DAC with $V_{ref} = 5$ V, the step size (resolution) is $V_{step} = V_{ref} / (2^n: 1) = 5 / 255 = 19.6$ mV.
- To output 3.0V, you need digital value $D = \lfloor V_{out} \times (2^n: 1) / V_{ref} \rfloor = \lfloor 3.0 \times 255 / 5 \rfloor = 153$.
- Actual output is $V_{actual} = 153 \times 5 / 255 = 3.0$ V exactly.
- With a 12-bit DAC ($2^{12}: 1 = 4095$), step size shrinks to $5 / 4095 = 1.22$ mV -- 16× finer than 8-bit, enabling smooth audio waveforms where 8-bit would sound grainy.
Major section
Quantization Error in DAC
Quantization appears because an N-bit DAC can produce only one of $2^N$ code levels.
- Increasing bit depth reduces that vertical step; increasing update rate reduces the time between code changes but does not create new voltage levels.
- A low-pass filter can attenuate step edges and PWM carrier energy, yet it also changes bandwidth, settling time, and load response.
- Problem:: DAC output is not truly analog - it's discrete steps.
Deck summary
Key takeaways
The computer holds a number, but the lamp needs voltage, current, and safe timing.
- A digital-to-analog converter (DAC) means a circuit that turns a number into a voltage or current.
- The mathematical gist.: An 8-bit endpoint DAC on 5 V has step $q=5/255=19.6$ mV and code 153 gives 3.00 V.
- The drawing communicates dAC conversion contract from bounded digital code through reference and transfer function to measured analog output.
- For an 8-bit DAC with $V_{ref} = 5$ V, the step size (resolution) is $V_{step} = V_{ref} / (2^n: 1) = 5 / 255 = 19.6$ mV.
Retrieval practice
Recall check 1 of 2
Voltage Vera says: answer from memory, then check your reasoning.
Q1A plant lamp receives a PWM command. What should the designer examine to predict its physical output?
Show answer
Answer: C PWM creates pulses that the load or filter averages; the load’s response matters.
Retrieval practice
Recall check 2 of 2
Voltage Vera says: answer from memory, then check your reasoning.
Q2A design smooths PWM pulses into an analog-like control signal. What choice does the chapter ask the learner to evaluate?
Show answer
Answer: B The chapter compares output methods and the trade-off introduced by filtering pulses.
Print reference
Answers
Answer key.
- C · PWM creates pulses that the load or filter averages; the load’s response matters.
- B · The chapter compares output methods and the trade-off introduced by filtering pulses.