Digital to Analog Converters in Electronic Circuits
Learn about Digital to Analog Converters (DACs) and how they convert digital signals to analog voltage or current outputs. Derive equations, analyze binary-weighted resistor circuits, and calculate Vout for different scenarios using examples.
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Electronic branch Fourth Class Interface Circuits Design Digital to Analog Converters Asst. Lec. Lubna A. Alnabi
Digital to Analog Converters What is the D/A? why is it needed? Do we always need it? (DAC) converts a digital signal or values to an analog voltage or current output.
Derive the equation for Vout for a binary weighted resister with Rf=R/2. ????= ? ?? ?1 ?+?2 2?+?3 ?? = ?? 4?+ 2? 1? IF ??= ?/2 ?1 2+?2 4+?3 8+ ?? ????= 2? For example, a 4-Bit converter yield ????= ????( ?3 Where b corresponds to Bit-3, b to Bit-2, etc. 1 2+ ?2 1 4+ ?1 1 8+?0 1 16)
Derive the equation for Vout for a binary weighted resister with Rf=R/3. Draw the block- diagram of a binary-weighted resistor cct. ????= ? ?? ?1 ?+?2 2?+?3 ?? = ?? 4?+ 2? 1? IF ??=? 3 ?1 3+?2 6+?3 12+ ?? ????= 2? For example, a 4-Bit converter yield ????= ????( ?3 Where b corresponds to Bit-3, b to Bit-2, etc. 1 3+ ?2 1 6+ ?1 1 12+?0 1 24)
Derive the equation for Vout for a binary weighted resister with Rf=R/6. ????= ? ?? ?1 ?+?2 2?+?3 ?? = ?? 4?+ 2? 1? IF ??=? 6 ?1 6+?2 12+?3 24+ ?? ????= 2? For example, a 4-Bit converter yield ????= ????( ?3 Where b corresponds to Bit-3, b to Bit-2, etc. 1 6+ ?2 1 12+ ?1 1 24+?0 1 42)
Find Vout for a binary weighted resistor D/A with Vref=5 Volts, and codeword = 101111 For a 6-Bit converter yield ????= ???? ?5 ????= 5 1 1 1 2+ ?4 1 4+ ?3 1 8+ ?2 1 16+ ?1 16+ 1 1 32+?0 32+ 1 1 64 1 64= -3.6718 2+ 0 1 1 8+ 1 1 1 4+ 1
Find Vout for a binary weighted resistor D/A with Vref=3.3 Volts, and codeword = 101101 For a 6-Bit converter yield ????= ???? ?5 ????= 3.3 1 1 1 2+ ?4 2+ 0 1 1 4+ ?3 4+ 1 1 8+ ?2 8+ 1 1 16+ ?1 1 16+ 0 1 32+?0 1 32+ 1 1 64 1 1 64=-2,3203
Derive the equation of Vout in a R-2R ladder D/A, draw the cct and the minimizations and show the equivalent resistors and voltage markings as well. ??? =2? 2? 2? + 2?= ? ?+??2 =1 ? ?3 = ?2 =1 ?1 =1 ?3 =1 2 ?2 2 ?1 2 ???? 1 2 ?1 =1 1 2 (1 2 ???? ) =1 8 ???? 2 2 ?2 =1 ?1 =1 4 ???? 2 ????
???? =IR ???? 2? ???? 4? ???? 8? ???? 16? ????= ? ?3 + ?2 + ?1 + ?0 Where b corresponds to Bit-3, b to Bit-2, etc. For a 4-Bit R-2R Ladder 1 2+ ?2 1 4+ ?1 1 8+ ?0 1 16 ????= ???? ?3 For general n-Bit R-2R Ladder or Binary Weighted Resister DAC ????= ???? ?1 2
Find Vout for an R-2R ladder D/A with Vref=3.3 Volts, and codeword = 101101 1 2+ ?4 1 4+ ?3 1 8+ ?2 1 16+ ?1 1 32+ ?0 1 64 ????= ???? ?5 ????= 3.3 1 1 2+ 0 1 4+ 1 1 1 16+ 0 1 32+ 1 1 64 8+ 1 =-54.914
Find Vout for an R-2R ladder D/A with Vref=5 Volts, and codeword = 101101 1 2+ ?4 1 4+ ?3 1 8+ ?2 1 16+ ?1 1 32+ ?0 1 64 ????= ???? ?5 ????= 5 1 1 2+ 0 1 4+ 1 1 1 16+ 0 1 32+ 1 1 64 8+ 1 =-3.5156
Find Vout for an R-2R ladder D/A with Vref=3.3 Volts, and codeword = 101101, (assume the switch that is responsible for the LSB is not working and it is stuck in the open state). 1 2+ ?4 1 4+ ?3 1 8+ ?2 1 16+ ?1 1 32+ ?0 1 64 ????= ???? ?5 ????= 3.3 1 1 2+ 0 1 4+ 1 1 1 16+ 0 1 32+ 0 1 64 8+ 1 =-2.2687
