# İkili Ağırlıklı DAC / Binary Weighted DAC

Binary-weighted digital-to-analog converters are a type of data converter that converts a digital binary number into an equivalent analog output signal proportional to the value of the digital number.

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**Digital-Analog Converters,** or **DAC** more commonly known as Analog-Digital Converters, which we looked at in the previous lesson, are the opposite.DACs convert binary or non-binary numbers and codes into analog numbers in proportion to the value of the output voltage (or current) digital input number.For example, it can have a 4-bit digital logic circuit that converts a DAC to a voltage output ranging from 0 to 10V, with ranges from 0 to_{1111} _{2}(0 and F 16).

Converting an "n"-bit digital input code from 0 to an equivalent analog output voltage between some V_{MAX} values can be done in several ways, but the most common and easily understood conversion methods use weighted resistors and a collection amplifier, or an R-2R resistance ladder network and operational amplifier.Both *digital to analogue conversion* methods produce a weighted total output, which contributes a different "weighted" amount to signal output, the weights determined by the resistance values used in stair networks.

In our tutorial section on Transactional Amplifiers, we found that an inverter uses negative feedback to reduce open loop gain, A _{OL,} and does so by feeding part of the output signal back into the input.This input voltage_{is} detected by the translating amplifier, which is directly connected by its converter input with a resistor R in V In, and this closed-loop voltage gain, as shown in a V _{(CL),} these two resistance ratios.

## Inverting the Transactional Amplifier Circuit

Thus, by changing the R _{F} or R _{IN} values, we can change the closed loop gain of the op-amp and therefore the V _{OUT} (I _{F} * R _{f)} value.) for a specific input signal.Here we used a single input voltage signal in this example of inverting transactional amplifier, but if we added another input resistance to combine two or more analog signals into a single output, what would be the effect on the circuit and its gain.

## Digital-Analog Converter Collection Amplifier

By connecting multiple inputs to the negative terminal of the transactional amplifier, we can convert the single input circuit from above to an *aggregation amplifier* or, more precisely, a "voltage amplifier" circuit that reverses the sum.

As negative feedback generated by feedback resistance, R _{K} is isolated from each other in the total of all inverted input signals combined with an effective electrical output, tilting the op-amp inverter input with zero potential.Thus, a collection amplifier in invert mode will produce the negative sum of any number of input voltages, while a non-inverted aggregation amplifier will produce the positive sum of any number of input voltages.Consider the circuit below.

In the aggregation amplifier circuit above, the output voltage (V _{OUT)} is proportional to the sum of four input voltages, V _{IN1} , V _{IN2} , V _{IN3} and V _{IN4,} and we can change the original equation for the inverted amplifier configuration. to take into account these four new input values as follows, click

Next, we can see that the output voltage is an inverted, scaled sum of four input voltages, since each input voltage is multiplied by its corresponding gain and added to the next to produce the total output.If all resistors are the same and equal value, that is: R _{F} = R _{1} = R _{2} = R _{3} = R _{4} , then each input channel will have a closed loop voltage gain of union (1). the output voltage is simply given as follows:

V _{OUTPUT} = –( V _{INTRODUCTION1} + V _{INTRODUCTION2} + V _{INTRODUCTION3} + V _{INTRODUCTION4} )

Now, assuming that the four inputs of the aggregation amplifier are binary inputs with voltage values of 0 or 5 volts (LOW or HIGH, 0 or 1), and double the resistance values of each input resistance compared to the previous one, we can produce an output condition that will be the weighted sum of these four input voltages, which form the basic circuit for the 4-bit dual-weighted digital-analog converter or the 4-bit weighted D/A converter.

A, B, C, D and construction R, with four collections of input labelling _{F} four inputs from 1kQ to 8kΩ resistances (or many), = 1kQ, can perform a simple 4-bit dual-weight analog-to-digital converter circuit as shown.

## 4-bit Dual Weighted Digital-Analog Converter

For a 4-bit binary number, there are 2 ^{4} = 16 possible combinations, or 0000 _{2} to 1111 _{2,} which corresponds to the 0 to 15 decimal place, respectively.If we double the weight of each input bit compared to the other, we get ^{a} binary code ratio of 8-4-2-1 corresponding to 2 ^{3} , 2 2 , 2 1 and 2 ^{} ^{0} .

So if we adjust the input resistance of "D" to 1kΩ, "C" input resistance to 2kΩ (i.e. twice the D), the input resistance of "B" to 4kΩ (double C) and "A" input resistance, R would be recalibrated 8kΩ (double B), 1k, then the 4-bit dual transfer characteristic would be a digital-analog converter.

## 4-bit DAC Transport Characteristic

Thus, if a TTL voltage of +5 volts (logic 1) is applied to the input of the aggregation amplifier, we can see that the V _{D} representing the most important bit (MSB) will be R _{F} /R _{4} = gain.1kΩ/1kΩ = 1 (unit).Thus, with the 1000 4-bit binary code applied, the output of the digital-to-analog converter circuit will be -5 volts.Similarly, if +5 volts (logic 1) is applied to the V _{C} input of the aggregation amplifier, the gain of the op-amp will be R _{F} /R _{3} = 1kΩ/2kΩ = 1/2 (one half).Thus, the 4-bit binary code of the 0100 will produce an analog output voltage of -2.5 volts.

Again, with a "1" logic applied V _{B} to the input of the aggregation amplifier, the gain of op-amp will be R _{F} /R 2 = 1kΩ/4kΩ = _{1/4} (quarter) with 4-bit binary code producing 0010. An output voltage of -1.25 volts and finally a logic "1" applied to the input of the aggregation amplifier is _{} "1", representing the least significant bit (LSB), so the gain of the op-amp will be R _{F} /R _{1} = 1kΩ/. 8kΩ = produces an output voltage of -0.625 volts (12.5% resolution) with the 4-bit binary code of 1/8 (one in eight) 0001.

The resolution of this simple 8-4-2-1 dual-weighted digital-analog converter will produce an output voltage change of 0.625 volts per binary 1-bit change, and we can express this output voltage change as follows. table.

## 4-bit Dual Weighted D/A Converter Output

Digital Inputs | V _{OUT} Expression | V _{OUTPUT} | |||

NS | C | B | A | 1*V _{D} + ^{1} / _{2} *V _{C} + ^{1} / _{4} *V _{B} + ^{1} / _{8} *V _{A} | In volts |

0 | 0 | 0 | 0 | 0*5 + 0*5 + 0*5 + 0*5 | 0 |

0 | 0 | 0 | 1 | 0*5 + 0*5 + 0*5 + ^{1} / _{8} *5 | –0.625 |

0 | 0 | 1 | 0 | 0*5 + 0*5 + ^{1} / _{4} *5 + 0*5 | -1.25 |

0 | 0 | 1 | 1 | 0*5 + 0*5 + ^{1} / _{4} *5 + ^{1} / _{8} *5 | –1.875 |

0 | 1 | 0 | 0 | 0*5 + ^{1} / _{2} *5 + 0*5 + 0*5 | –2.50 |

0 | 1 | 0 | 1 | 0*5 + ^{1} / _{2} *5 + 0*5 + ^{1} / _{8} *5 | –3.125 |

0 | 1 | 1 | 0 | 0*5 + ^{1} / _{2} *5 + ^{1} / _{4} *5 + 0*5 | –3.75 |

0 | 1 | 1 | 1 | 0*5 + ^{1} / _{2} *5 + ^{1} / _{4} *5 + ^{1} / _{8} *5 | –4.375 |

1 | 0 | 0 | 0 | 1*5 + 0*5 + 0*5 + 0*5 | –5.00 |

1 | 0 | 0 | 1 | 1*5 + 0*5 + 0*5 + ^{1} / _{8} *5 | –5.625 |

1 | 0 | 1 | 0 | 1*5 + 0*5 + ^{1} / _{4} *5 + 0*5 | –6.25 |

1 | 0 | 1 | 1 | 1*5 + 0*5 + ^{1} / _{4} *5 + ^{1} / _{8} *5 | –6.875 |

1 | 1 | 0 | 0 | 1*5 + ^{1} / _{2} *5 + 0*5 + 0*5 | –7.50 |

1 | 1 | 0 | 1 | 1*5 + ^{1} / _{2} *5 + 0*5 + ^{1} / _{8} *5 | – 8.125 |

1 | 1 | 1 | 0 | 1*5 + ^{1} / _{2} *5 + ^{1} / _{4} *5 + 0*5 | –8.75 |

1 | 1 | 1 | 1 | 1*5 + ^{1} / _{2} *5 + ^{1} / _{4} *5 + ^{1} / _{8} *5 | –9.375 |

In cases where all output voltages are negative due to the inverting input of the collection amplifier.

The resolution of the analog output voltage can be increased for a dual-weight digital-analog converter by increasing the number of binary numbers and the resistant collection network so that each resistance has a different weight.For example, an 8-bit DAC with TTL +5 input produces a resolution of 0.039 (1/128*V), while a 12-bit DAC will be 0.00244 (1/2048*V) volts (1 LSB) per step. ) change the input binary (or non-binary) code.

Obviously, the disadvantage here is that a binary-weighted resistance DAC requires a wide range of high-precision resistors (one per bit) for a "n"-bit DAC, which makes it practical (and expensive) for converters with more than a few bits.However, we can expand the idea of this dual-weighted digital-analog circuit configuration using different value resistors one step further by converting the R-2R resistance ladder, which requires only two precise resistance values, to dac, that is, R and 2R.

In the next content about **Digital-Analog Converters,** we will look at how *the R-2R Digital-Analog Converter* uses only two resistance values to convert a digital binary number into analog voltage output .