BEng Electronic Engineering
DIGITAL ELECTRONICS
Lecture 3 - Digital to Analogue Converters (Part 3)
Dr. Martin Hope
m.d.hope@salford.ac.uk
AIM
To understand the meaning of
parameters commonly quoted to
specify converter performance and
look at some less common
conversion methods
Objectives
• Understand the meaning of quoted DAC
parameters ant their effects on the outputs of
the converter
• Look at some other less direct methods of
achieving Digital to Analogue Conversion
DAC Parameters
There are a number of parameters associated with Digital
to Analogue converters that you will often see quoted in
data sheets and which you should understand in order to
assess the relative performance of the converters
• Quantisation error
• Linearity error
• Differential non-linearity
• Setting time
Quantisation Error
An ideal Digital to Analogue converter should produce a
linear voltage output line. In practice this is impossible
because of the quantised nature of the digital input
V
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Quantisation Error
On removing all other errors we are
still left with the quantisation error
16
15
14
13
12
0.5 LSB
11
0.5 LSB
10
9
8
7
6
5
± 0.5LSB
4
3
2
1
0
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Linearity Error
Linearity error is a measure of the worst case difference between the
voltage output of the converter and the ideal voltage.
LSB
16
Bit 0: +0.5 LSB
15
14
13
12
Bit 1: -0.5 LSB
11
0.5
LSB
-1
-2
-1.5
LSB
-1
-1.5
-2
LSB
00 LSB
++
---1.5
0.5
10
Bit 2: -1.5 LSB
9
8
7
Bit 3: 0 LSB
6
5
4
LINEARITY
ERROR
-2 LSB
3
2
1
0
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Differential Non - Linearity Error
Differential non-linearity error is a measure of the worst case
difference between the expected voltage output and the actual
voltage output.
LSB
16
15
Bit 0: +0.5 LSB
14
13
12
Bit 1: -0.5 LSB
+0.5
LSB
+0.5
+0.5
-1
LSB
LSB
-1.5
-1.5
LSB
+0.5
+
-1
0.5LSB
LSB
+0.5
LSB
+1.5
11
10
Bit 2: -1.5 LSB
9
8
7
Bit 3: 0 LSB
6
5
4
3
2
1
0
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
DIFFERENTIAL
NON-LINEARITY
ERROR
± 1.5 LSB
Setting Time
This is the amount of time it takes the output of the DAC to settle to
within +/-0.5LSB of the new output when the digital input changes
Settling
Time
1ms
LSB
16
15
14
13
12
11
10
1LSB
9
8
7
6
5
4
3
2
1
0
1ms
2ms
3ms
4ms
5ms
6ms
7ms
8ms
9ms
10ms
11ms
12ms
13ms
14ms
15ms
16ms
Time
Pulse Width Modulation
This uses a counter and comparator to generate waveform with
variable duty cycle
0
1
0
1
0
1
LOW PASS
A
A>B
B
0
1
0
1
1
0
1
0
1
FILTER
Frequency to Voltage Conversion
This simply uses the distance between digital pulses
of fixed width to generate a varying d.c. output
LOW PASS
FILTER
-0.5 LSB
0 LSB
0110
0111
1000
1001
0 LSB
+0.5 LSB
0101
-0.5 LSB
0 LSB
0100
-1 LSB
-0.5 LSB
0011
-1.5 LSB
-1 LSB
0010
+1 LSB
+1.5 LSB
0001
+0.5 LSB
+1 LSB
LSB
+0.5 LSB
Linearity Error - Worked Example 1
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0000
1010
1011
1100
1101
1110
1111
+0.5 LSB
+0.5 LSB
+0.5 LSB
-2.5 LSB
+0.5 LSB
+0.5 LSB
+0.5 LSB
-1 LSB
+0.5 LSB
+0.5 LSB
+0.5 LSB
-2.5 LSB
+0.5 LSB
LSB
+0.5 LSB
+0.5 LSB
Non – Linearity Error - Worked Example 2
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
ANY QUESTIONS?