Chapter 4 Part I: D/A Concepts & Converters

What is a box-car signal?

- A boxcar signal is obtained from a digital signal by sending each N-bit digital sample to a DAC, where it is converted into the equivalent analog signal whose value is maintained until the next sample is converted in the DAC. - A boxcar signal is related to the DIGITAL samples, and not to the discrete samples.

What is a digital data sample?

- A digital data sample refers to an N-tuple which ranges over a finite number of states, and is the quantized form of the discrete sample, representing the analog signal point.

What is a digital signal?

- A digital signal is obtained from a discrete signal by quantizing each discrete value to a sample with the desired number of bits. - The number of bits is determined from the noise level and other considerations.

What is a discrete signal?

- A discrete signal is obtained from an analog signal that is sampled at a rate that is slightly higher (10%) than the Nyquist sampling frequency.

What is a glitch?

- A glitch is an anomalous spike at the output of the D/A converter when the input code changes. - The glitches are due to non-simultaneous opening and closing of switches during transitions from one digital code to another.

When does a negative glitch occur?

- A negative glitch occur if 011 goes to 000 (all switches open) prior to 100. - Break before make (BBM)

When does a positive glitch occur?

- A positive glitch occurs if 011 goes to 111 (all switches close) prior to 100. - Make before break (MBB)

What is a quantization step?

- A quantization step is the distance between quantization levels.

What is an analog signal?

- An analog signal is defined as a continuous (or discontinuous) function of time or space defined at all time instants as well as for all magnitudes within the full-scale.

How do we determine the cut-off frequency?

- Antialiasing filtering is required to establish the cut-off frequency.

What must the sampling frequency be greater than the Nyquist frequency?

- Because we could get really unlucky, e.g. reconstructing a DC signal instead of a sine wave.

How can we solve the monotonicity when summing over current?

- By using a potentiometric voltage subdivision. - Even if there are errors in matching the resistors, monotonicity is always guaranteed!

What is aperture time?

- Conversion of each sample must happen within the aperture time in which the input signal does not change by more than one quantization step.

What is D/A conversion?

- D/A conversion is a process involving mapping of n-bit digital code (binary) into discrete electrical physical quantities.

In practice, how should the sampling frequency be chosen?

- In practice the sampling frequency must be greater than the Nyquist frequency.

Give examples of analog data.

- Physical quantities such as pressure, motion, acceleration that can be represented by electric quantities current and voltage.

What is settling time?

- Settling time is defined as the time elapsed from the application of a full-scale binary code input to the time when the D/A converter output reaches a quasi steady state, within specified limits.

When must the signal from a sensor be amplified?

- Sometimes the signal originating from a sensor may be very small. - The range of the signal must match the range of the A/D converter, and so the signal must be amplified. - This amplification may introduce noise and distortion.

What is the Nyquist theorem?

- The Nyquist theorem states that the input signal to the ADC can be reconstructed iff the signal is sampled at twice the cut-off frequency.

In what forms can we have an analog signal?

- The signal may be in the form of either electric current or electric voltage. - The form of the signal affects how the signal is transmitted from a sensor to the ADC. - This signal can be unipolar or bipolar.

What are the problems with summing over current?

- The weighted current source and R-2R D/A converters cannot guarantee monotonic output (doesn't always increase linearly w/ level). - For example, if the MSB resistor is slightly bigger than the required value, then the output voltage generated by 100 may be smaller than the output voltage generated by 011.

What is the Nyquist sampling frequency?

- Twice the cut-off frequency, measured in samples per second.

Give an example of a deglitching circuit.

- While a new digital signal is being captured by the flip flop, the S&H device is disconnected from the DAC, and holds the previous value of the DAC. - After the settling time of the DAC, the S&H connects back to the DAC. - The duration of the clock pulse must be longer than the settling time of the DAC.

What is the smallest resolvable increment in time and magnitude for an analog signal?

0, 0

What is the smallest resolvable increment in time and magnitude for a boxcar signal?

0, Q = FS/2^n

How many different states are there in a digital signal?

2^N

What are the advantages\disadvantages of the common base implementation of the weighted current sources DAC?

Advantages: -------------- - simplicity (n resistor, n switches) - high speed Disadvantages: ---------------- - large range of resistor values (2^n to 1) - high resistor values are not suitable for high resolution converters

What are the advantages/disadvantages of the R-2R ladder D/A (binary chopping)?

Advantages: -------------- - still simple (n switches) - only two values of resistors (R, 2R) - for high speed applications, relatively low resistor values can be used - can use laser trimming of the resistors for high precision

What is the smallest resolvable increment in time and magnitude for a discrete signal?

Ts = 1 / fs, 0

What is the smallest resolvable increment in time and magnitude for a digital signal?

Ts = 1/fs, Q = FS/2^n

What is the full-scale?

V_max - V_min

What is signal to noise range (SNR)?

V_max MAX / N_max V_max MAX: the signal level N_max: system noise level

How is a signal transmitted to the ADC if it is in the form of electric voltage?

absolute or differential lines

What is the resolution in time and magnitude of a discrete signal?

fs = 1/Ts, infinite

What is the resolution in time and magnitude of a digital signal?

fs, 1/Q

What is allowed when going from the discrete domain to the digital domain (in terms of mapping)?

i) each n-tuple is mapped to a different value ii) multiple n-tuples are mapped to the same value NOT ALLOWED: the same n-tuple is mapped to different values

What are desirable characteristics of an ADC?

i) high accuracy: linearity and other errors should be the smallest possible ii) high resolution: many bits, Q must be larger than the noise signal level iii) fast conversion iv) environmentally stable v) monotonic

What types of DAC exist?

i) serial ii) parallel

How is a signal transmitted to the ADC if it is in the form of electric current?

in a current loo

What is the resolution in time and magnitude of a boxcar signal?

infinite, 1/Q

What is the resolution in time and magnitude of an analog signal?

infinite, infinite