Digital Circuits

Digital-to-Analog Conversion

13 questions By Tony R. Kuphaldt

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Question 10 of 13

What is meant by the word resolution in reference to an ADC or a DAC? Why is resolution important to us, and how may it be calculated for any particular circuit knowing the number of binary bits?

Reveal answer

The resolution of either a digital-to-analog converter (DAC) or an analog-to-digital converter (ADC) is the measure of how finely its output may change between discrete, binary steps. For instance, an 8-bit DAC with an output voltage range of 0 to 10 volts will have a resolution of 39.22 mV.

Notes:
Note that I did not hint how to calculate the resolution of a DAC or an ADC, I just gave the answer for a particular example. The goal here is for students to inductively “work backwards” from my example to a general mathematical statement about resolution.

There are actually two different ways to calculate the resolution, depending on the actual range of the converter circuit. For the answer given, I assumed that a digital value of 0x00 = 0.00 volts DC and that a digital value of 0xFF = 10.00 volts DC. If a student were to calculate the resolution for a circuit where 0xFF generated an output voltage just shy of 10.00 volts DC (e.g. an R-2R ladder network where V_ref = 10 volts DC, and a full-scale binary input generates an output voltage just one step less than V_ref), the correct answer for resolution would be 39.06 mV.

You may want to bring up such practical examples of resolution as the difference between a handheld digital multimeter and a lab-bench digital multimeter. The number of digits on the display is a sure clue to a substantial difference in ADC resolution.
Question 11 of 13

This digital-to-analog converter (DAC) circuit takes a four-bit binary input (input terminals A through D) and converts it to an analog voltage (V_out). Predict how the operation of this circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):

Bilateral switch U₁ fails open:

Zener diode fails shorted:

Solder bridge (short) past resistor R₁:

Resistor R₆ fails open:

Reveal answer

Bilateral switch U₁ fails open: V_out same for all odd numbered input conditions as it is for next lowest even-numbered input condition (e.g. input value of 5 gives same output as input value of 4).

Zener diode fails shorted: V_out is nearly zero volts for any input condition.

Solder bridge (short) past resistor R₁: V_out saturates positive for any given odd-valued input condition.

Resistor R₆ fails open: V_out always saturated.

Follow-up question #1: is the arrow showing zener diode current drawn in the direction of electron flow or conventional flow?

Follow-up question #2: which input bit is the most significant (MSB) and which is the least significant (LSB)?

Notes:
Questions like this help students hone their troubleshooting skills by forcing them to think through the consequences of each possibility. This is an essential step in troubleshooting, and it requires a firm understanding of circuit function.
Question 12 of 13

The following circuit generates an analog output voltage proportional to the value of the binary input, using pulse-width modulation (PWM) as an interim format. An eight-bit binary counter (CTR) continually counts in the üp” direction, while an 8-bit magnitude comparator (CMP) checks when the 8-bit binary input value matches the counter’s output value. The AND gate and inverter simply prevent the S-R latch from being “set” and “reset” simultaneously (when both A and B are maximum, both at a hex value of $FF), which would cause the output to be “invalid” when S and R were both active, and unpredictable when both S and R inputs returned to their inactive states:

Explain how this circuit works, using timing diagrams if necessary to help show the PWM signal at $\bar{Q}$ for different input values.

Reveal answer

Here is a timing diagram to help get you started on a complete answer:

I’ll leave it to you to explain the relationship between the input value (A), the PWM duty cycle, and the analog output voltage.

Notes:
This circuit provides students with an interesting exercise in timing analysis, as well as being a simple means of converting large binary values into analog output voltages without resorting to using large resistor networks.