Binary Weighted Resistor Type DAC CMOS DESIGN

12 min readJun 8, 2021

1. About the Tool Used

Simulation software used is NI MultiSim,

It is developed by National Instruments; it can be operated on Windows OS only.

NI Multisim is an electronic schematic capture and simulation program which is part of a suite of circuit design programs, along with NI Ultiboard. Multisim is one of the few circuit design programs to employ the original Berkeley SPICE-based software simulation. Multisim was created by a company named Electronics Workbench, which is now a division of National Instruments. Multisim includes microcontroller simulation (formerly known as MultiMCU), as well as integrated import and export features to the printed circuit board layout software in the suite, NI Ultiboard.

Multisim is widely used in colleges and industries for circuits education, electronic schematic design, and SPICE simulation.

Multisim™ software integrates industry-standard SPICE simulation with an interactive schematic environment to instantly visualize and analyze electronic circuit behavior. Its intuitive interface helps educators reinforce circuit theory and improve retention of theory throughout the engineering curriculum. By adding powerful circuit simulation and analyses to the design flow, Multisim™ helps researchers and designers reduce printed circuit board (PCB) prototype iterations and save development costs.

Basically, it is used to develop products before hardware development and integration on PCBs, it is easy to use and analyze, it is user-friendly and interactive.

It has various features such as AC sweep, DC sweep, transient analysis, interactive analysis, and more.
It has a large database and all the circuit components found in the market can be used. Even our own database can be created.
Pre-existing database of model devices, the parameters can be changed for analysis purpose.
Digital design, PCB design, and breadboard can be visualized using this software tool.

2. INTRODUCTION

2.1. What is a DAC?

The world is analog in nature. However, computational devices like processors and controllers can only understand the digital representation of data. Thus, in order t make these devices compatible with the world of data, interconversion between analog and digital data is important. The devices used for this purpose are Analog to Digital Converter (ADC) and Digital to Analog Converter (DAC).

A digital-to-analog converter (DAC) takes a digital code as its input and produces an analog voltage or current as its output. This analog output is proportional to the digital input.

Digital to Analog conversion involves transforming the computer’s binary output in 0’s and 1’s (1’s typically = 5.0 volts) into an analog representation of the binary data.

A DAC accepts n binary input and Vmax as the voltage maximum reference and outputs an analog voltage.

In this article, we will learn how a DAC works and how it can be used in our designs.

2.2. Types of DAC

Summing Amplifier

Since digital to analog conversion is simply a weighted sum of the binary input, a circuit called a summing amplifier is used. This is basically an op-amp amplifier with multiple resistors connected to one input. The junction where the resistors meet is called the summing junction or the virtual ground. The binary input goes into the resistors and the analog output is obtained on the output of the op-amp. What makes this circuit work is the resistors — each resistor has to be carefully chosen and matched to obtain an accurate analog output. The more bits you have, the more different values of resistors you need — and these are not always practical. The limitations can be overcome by using the next method.

Binary Weighted Resistor

In this DAC, Weighted Resistors Are Used to Distinguish Each Bit from The Most Significant to The Least Significant. The circuit utilizes an op-amp in inverting mode and a weighted resistor circuit to implement digital to analog conversion.

R-2R Ladder

This is the simplest type of DAC and needs only two resistor values arranged in a ladder. You can think of this as a somewhat complex voltage divider, though the math is quite complex. The binary input goes into the 2R resistors and the output is obtained at the bottom of the ladder.

Current Steering DAC

The Current steering DACs are the more commonly used architecture because of their small size and simplicity, high resolution, and high speed. Based on the binary principle, current sources are scaled. Here for the ith current source, the output current is equal to the 2i*I, Where I = Least significant bit (LSB) current. For the design of DAC, various switches like NMOS, PMOS, and transmission gates are explored. Characteristics of switching elements are one of the prominent factors for the dynamic nonlinearity of DAC

PWM DAC

This is the type of DAC that most of us have used without even knowing it! The popular Arduino microcontroller has the capability to output analog signals using a PWM signal. At the outset, the PWM signal looks like a binary waveform with only high and low peaks with a variable duty cycle (ratio of on time-to-time period). However, this is intended to be used with an RC filter to convert the PWM signal into a voltage value by filtering out the AC component and leaving behind the DC component. The voltage output is proportional to the duty cycle of the input — the higher the duty cycles the greater the output voltage of the filter.

2.3. Applications of DAC

Circuit Components

Voltage Controlled Amplifier

Digital Input, External Reference Voltage as Control.

Digitally Operated Attenuator

External Reference Voltage as Input, Digital Control.

Programmable Filters

Digitally controlled cut-off frequencies.

Digital Audio

Function Generators and CRO

Motor Controllers

3. LITERATURE SURVEY

A DAC will be a framework that changes over a computerized flag into a simple flag. A simple computerized converter (ADC) plays out the turnaround capacity. Any time a signal is converted from one format to another; there is a potential loss of quality. In this manner, it is essential to have an astounding DAC whether you are changing over sound or video signals. Similar remains constant when playing out the contrary change, which requires a simple to a computerized converter, or ADC.

There are two types of DAC using Op-Amps namely Weighted Resistor Type and R2R Ladder Type.

R2R Ladder Type DAC

The theory of the R-2R ladder network is that fundamental current derivative terminated either input resistor. The reverse signal confrontation two available paths another moderate current. These flows back approaching another half of magnitude don’t reach the operational amplifier, and therefore have in reaction on the output voltage. The overall resistances of both paths are the same (also R-2R), so the entering current division equally one and the other paths. The moderate that returns the path approaching for operational amplifier on the ladder consider overcome the output. The inverting input of the op-amp is virtual. Current flowing in the component of the ladder network is then directed by switch positions.

The output is given by:

Binary Weighted Resistor Type DAC

In the weighted resistor type DAC, each digital level is converted into an equivalent analog voltage or current.

It consists of a parallel binary weighted resistor bank and a feedback resistor Rf.
The switch positions decide the binary word (i.e., B1 B2 B3…Bn)

Let us analyze the circuit using normal analysis concepts used in the op-amp. When the switches are closed the respective currents are flowing through resistors as shown in the circuit diagram above.
Since the input current to the op-amp is zero, the additional current flows through the feedback resistor.
∴I=I1+I2+I3+ …………+In

The inverting terminal of an op-amp is virtually at ground potential.

The number of switches each bit is applied for the input signal. The binary-weighted resistor is analogous to inversely proportional to the mathematical significance digital signal. Vref is a reference voltage. The voltage surface at any network resistance is identical to the addition of the current access incomplete by the addition of the transmission connected to the mode. Binary weighted resistor Consider that the resistor R1, R2, R3…… Rn.

The main components used are an operational amplifier and a Weighted Resistor network. Op-amp is made up of two stages. The first stage of op-amp consists of a differential amplifier and the second stage consists of a common source amplifier. The first stage is used to get high gain and the second stage increases output swing and gain of the first stage.

The various parameters of a DAC are:

Resolution

Resolution is characterized as the quantity of various simple yield voltage levels that can be given by a DAC or on the other hand goals is characterized as the proportion of an adjustment in yield voltage coming about for a difference in 1 LSB at the advanced information. Just, goals are the estimation of LSB.

Linearity

Linearity mistake is the most extreme deviation in step measure from the perfect advance size. Some D/A converters are having a linearity mistake as low as 0.001% of full scale. The linearity of a D/A converter is characterized as the accuracy or precision with which the advanced info is changed over into a simple yield. A perfect D/A converter produces a square with augmentations or step sizes at yield for each adjustment in equivalent additions of parallel info.

Monotonicity

A Digital Analog converter is said to be monotonic if the simple yield increments for an expansion in the computerized information. A monotonic characteristic is essential in control applications. Otherwise, it would lead to oscillations. If a DAC has to be monotonic, the error should be less than ± (1/2) LSB at each output level. Henceforth all the D/A converters are planned with the end goal that the linearity mistake fulfills the above condition. At the point when a D/A Converter doesn’t fulfill the condition portrayed above, at that point, the yield voltage may diminish for an expansion in the parallel information.

Conversion Time

It is the time taken for the D/A converter to produce the analog output for the given binary input signal. It depends on the response time of switches and the output of the Amplifier. D/A converter's speed can be defined by this parameter. It is also called setting time.

Settling time

It is one of the important dynamic parameters. It represents the time it takes for the output to settle within a specified band ± (1/2) LSB of its final value following a code change at the input (Usually a full-scale change). It relies upon the exchanging time of the rationale hardware because of inner parasitic capacitances and inductances. An average settling time ranges from 100 ns to 10 us relying upon the word length and sort of circuit utilized.

Stability

The capacity of a DAC to deliver a steady yield all the time is called Stability. The execution of a converter changes with a float in temperature, maturing, and control supply varieties. So, every one of the parameters, for example, balance, gain, linearity mistake, and monotonicity may transform from the qualities Specified in the datasheet. Temperature affectability characterizes the strength of a D/A converter

Thus, the straightforward (DAC) is a converter and is used to change over discrete signal input. A Binary Weighted Resistor Type DAC uses an op-amp and weighted resistor circuit to convert digital input of length n to an analog voltage.

4. Binary Weighted Resistor DAC’s CMOS Implementation

4.1. Principle

A DAC converts an abstract finite-precision number (usually a fixed-point binary number) into a physical quantity (e.g., a voltage or a pressure). In particular, DACs are often used to convert finite-precision time series data to a continually varying physical signal.

4.2. Construction

A Binary Weighted Resistor Type DAC consists of an Op-Amp operating in inverting mode and Binary Weighted Resistor Network consisting of weighted resistances and SPDT (Single Pole Dual Throw) Switches. A low pass filter is used to smoothen the output.

4.3. Circuit Diagram

4.4. Working

In a Binary Weighted DAC, n binary inputs are used to represent a word as follows:

Each Binary Bit can Toggle between Ground and Vref subsequently contributing to the Binary Word. Each bit has a weighted resistor whose value depends on the weight of that particular bit in Binary.

The Bits produce an equivalent current output through the resistors which is fed to the inverting terminal of the op-amp which acts as a trans-resistance amplifier producing equivalent voltage. Thus, an n-bit Binary Word is converted to an equivalent voltage.

The output voltage of the DAC for a particular Binary Word can be calculated as follows:

More generally,

Final Vout = Vout * Resolution

Where,

4.5. CMOS Circuit Design

Differential and Common Source Stage Amplifiers

A differential amplifier multiplies the voltage difference between two inputs (Vin+ — Vin-) by some constant factor Ad, the differential gain. It may have either one output or a pair of outputs where the signal of interest is the voltage difference between the two outputs. A differential amplifier also tends to reject the part of the input signals that are common to both inputs (Vin+ + Vin-)/2. This is referred to as the common-mode signal. This stage provides high gain.

A Common Source Amplifier has its source terminal grounded and it acts as the common terminal for all measurements. The input is applied to the base terminal and output is taken across the emitter terminal. It offers a very high input impedance and a finite output impedance. This stage provides a good output swing and increases CMRR.

Current Mirror Circuits

A current mirror is a circuit designed to copy a current through one active device by controlling the current in another active device of a circuit, keeping the output current constant regardless of loading.

The basic circuit of the transistor current mirror comprises two transistors, one of which has the base and collector connected and the other does not. The base connections of both transistors are then linked, as are the emitters which are also taken to the ground. In terms of the operation of the circuit, the base-emitter junction of TR1 acts like a diode because the collector and base are connected. The current into TRI is set externally by other components, and as a result, there is a given voltage built up across the base-emitter junction of TR1. As the base-emitter voltage on both transistors is the same, the current in one transistor will exactly mirror that of the second, assuming that both transistors are accurately matched. Therefore, the current flowing into TR1 will be mirrored into TR2 and hence into the load R1.

The mos current mirror circuits are based on the principle that, if the gate to source voltage of two identical MOSFETs is equal then the drain current flowing through them is equal.

4.6. Multisim Realization of the Circuit

The differential pair is biased by current mirrors, which acts as the active load too. Two current mirrors a PMOS current mirror (M3 & M5) and an NMOS current mirror (M6 &M8) are used instead of just one to increase the common-mode rejection ratio (CMMR) of the differential pair. The PMOS current mirror serves as a constant current source and the NMOS mirror, which sinks current, acts as an active load across which the first stage output is taken, thereby performing a differential to single-ended conversion in the process.

Common Source Amplifier is used to reduce the common-mode gain and thus increase CMRR.

4.7. Simulation Output

To simulate a real-time response, we have implemented a counter using square pulses of Increasing frequencies and connected these pulses to the Binary Inputs of the DAC as follows: