Solution: SPI 8-bit DAC

Given:

• DAC resolution = 8 bits
• Output range = 0–5 V
• SPI clock = 4 MHz

(i) SPI Timing and DAC Output

SPI is a synchronous serial protocol. The master provides the clock on SCLK, sends data on MOSI, and selects the DAC using chip select (CS).

Typical sequence:

CS ↓ → Send command/data bits on MOSI → Clock pulses → CS ↑ → DAC updates output

The exact sampling clock edge and timing depend on the DAC's SPI mode specified in its datasheet.

For an ideal 8-bit DAC, the input code ranges from:

$$0\text{ to }2^8-1=255$$

For a 0–5 V output using the common ideal endpoint convention:

$$V_{out}=\frac{D}{255}\times5$$

where $D$ is the decimal DAC code.

Thus:

• $D=0 \Rightarrow V_{out}=0$ V
• $D=255 \Rightarrow V_{out}=5$ V

The approximate voltage step is:

$$\frac{5}{256}=19.53\text{ mV}$$

The exact transfer function should follow the DAC datasheet if it uses a different reference/output convention.

(ii) Maximum Update Rate

An 8-bit DAC requires at least 8 clock cycles per update if the SPI frame contains only the 8 data bits.

SPI clock:

$$f_{SPI}=4\text{ MHz}$$

Therefore:

$$f_{update,max}=\frac{4\times10^6}{8}$$

$$\boxed{f_{update,max}=500,000\text{ updates/s}}$$

or:

$$\boxed{500\text{ kUpdates/s}}$$

Important practical note

If the DAC requires more than 8 bits per SPI frame—for example, command bits, address bits or control bits—the actual maximum update rate will be lower:

$$f_{update,max}=\frac{f_{SPI}}{N_{bits/frame}}$$

Final Answer

• DAC output: $V_{out}=\frac{D}{255}\times5$ V under the stated endpoint convention.
• Approximate LSB step: 19.53 mV.
• Maximum theoretical update rate for an 8-bit frame: 500 kUpdates/s.