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SEMINAR TOPIC:
R-2R LADDER DAC, Photo Electric Devices LED, LCD, Photo diode,
Expalin the 8085 pgm for binary division.
PRESENTED BY
,
SARAMBA KRISHNAN C.P
SHERUN ANEEV T.P
SHIBIN RAJ .A
SHONE JOHNSON
PHOTO ELECTRICAL DEVICES
Devices which give an electrical signal in response to visible, infrared, or
ultraviolet radiation
 A photoelectric cell, also called sometimes a phototube, electron tube, or
electric eye, is an electronic device that is sensitive to incident radiation,
especially visible light, which is used to generate or control an output of
electric current.
 During the latter half of the nineteenth century, many scientists and
engineers were simultaneously observing a strange phenomenon:
electrical devices constructed from certain metals seemed to conduct
electricity more efficiently in the daytime than at night.
 This phenomenon, called the photoelectric effect, had been noted years
earlier by French physicist Alexandre-Edmond Becquerel (1820–1891),
who had invented a very primitive device for measuring the intensity of
light by measuring the electrical current produced by photochemical
reactions.
 The devices, often called photoelectric cells, have the ability to convert
light signals into corresponding electric signals. The latter can then be
processed by conventional electronic equipment to produce desired
results. Photoelectric cells can do more than merely replace the human
eye.
 The photoelectric cells, have the ability to convert light signals into
corresponding electric signals. Photoelectric devices may be classified
according to the mechanism of their operation.
 The photoelectric effect is the process in which electromaganetic radiation
such as visible light, x rays, or gamma rays strike matter and cause an
electron to be ejected. The ejected electron is called a photoelectron.
 At the time that Becquerel was performing his experiments, it was
becoming evident that one metal in particular—selenium—was far more
reactive when exposed to light than any other substance. Using selenium
as a base, several scientists set out to develop a practical device for
measuring light intensity.
PHOTOELECTRIC EFFECT
 Electrical devices constructed from certain metals seemed to conduct
electricity more efficiently in the daytime than at night. This
phenomenon, called the photoelectric effect.
 The photoelectric effect is the emission of electrons when
electromagnetic radiation, such as light, hits a material
USES
 Photoelectric cells are used as switches (electric eyes), light detectors
(burglar alarms), devices to measure light intensity (light meters), and
power sources (solar cells).
PHOTO DIODE
 Photodiode is a semiconductor p–n junction device that converts light
into an electrical current.
 The current is generated when photons are absorbed in the
photodiode.
 Photodiodes may contain optical filters, built-in lenses, and may have
large or small surface areas. Photodiodes usually have a slower
response time as their surface area increases.
 The common, traditional solar cell used to generate electric solar
power is a large area photodiode.
PHOTO DIODE
 Type : -Passive
 Working principle :-Converts light into current
 Pin configuration :-anode and cathode
 Electronic symbol :-
 Photodiodes are similar to regular semiconductor diodes except that they
may be either exposed (to detect vacuum UV or X-rays) or packaged with
a window or optical fiber connection to allow light to reach the sensitive
part of the device.
 Many diodes designed for use specially as a photodiode use a PIN
junction rather than a p–n junction, to increase the speed of response.
 A photodiode is designed to operate in reverse bias.
OPERATION
 A photodiode is a PIN structure or p–n junction. When a photon of
sufficient energy strikes the diode, it creates an electron–hole pair.
This mechanism is also known as the inner photoelectric effect.
 Thus holes move toward the anode, and electrons toward the
cathode, and a photocurrent is produced. The total current through the
photodiode is the sum of the dark current and the photocurrent, so
the dark current must be minimized to maximize the sensitivity of the
device.
 DARK CURRENT: current that is generated in the absence of light
MATERIALS USED TO MAKE A PHOTO DIODE
 Material
Silicon
Germanium
Indium gallium arsenide
Lead(II) sulfide
Mercury cadmium telluride
Electromagnetic spectrum
wavelength range (nm)
190–1100
400–1700
800–2600
<1000–3500
400–14000
Only photons with sufficient energy to excite electrons across the material’s
bandgap will produce significant photocurrents.
Because of their greater bandgap, silicon-based photodiodes generate less
noise than germanium-based photodiodes
Binary materials, such as MoS2, and graphene emerged as new materials
for the production of photodiodes.
FEATURES
RESPONSE OF A SILICON PHOTO DIODE VS WAVELENGTH OF THE
INCIDENT LIGHT
Spectral responsivity:-
The spectral responsivity is a ratio of the generated photocurrent to incident light
power, expressed in A/W when used in photoconductive mode
Dark current:-
The dark current is the current through the photodiode in the absence of light,
when it is operated in photoconductive mode.
Response time:-
The response time is the time required for the detector to respond to an optical
input
Noise-equivalent power:-
Noise-equivalent power (NEP) is the minimum input optical power to generate
photocurrent, equal to the rms noise current in a 1 hertz bandwidth
APPLICATION
 Photodiodes are often used for accurate measurement of light
intensity in science and industry.
 Used as photoconductors, charge-coupled devices (CCD), and
photomultiplier tubes
 Devices such as compact disc players, smoke detectors, medical
devices
 Accurate measurement of light intensity in science and industry
 Various medical applications, such as detectors for computed
tomography , instruments to analyze samples (immunoassay), and
pulse oximeters.
LED & LCD
LED: In the simplest terms, a light-emitting diode (LED) is a semiconductor
device that emits light when an electric current is passed through it. Light is
produced when the particles that carry the current (known as electrons and
holes) combine together within the semiconductor material
LCD : In the simplest terms, A liquid crystal display(LCD) is thin, flat panel
display device used for electronically displaying information such as text,
images and moving picture.
LED
 A light emitting diode(LED) is essentially a PN junction opto semiconductor that
emits a monochromatic (single color) light when operated in a forward biased direction.
 LEDs convert electrical energy into light energy.
How does a LED work ?
 Light is a form of energy that is released from atoms. Light consists of many small energy
packets that have momentum but no mass. In the atom, electrons move in orbit around the
nucleus, and the electrons in different orbits have different amounts of energy. When
electrons descend from a higher orbit to a lower one energy is released in the form of
photons.
 The same thing happens inside the LED. Actually, an LED is a type of PN-junction diode
that uses a special type of semiconductor (such as gallium arsenide (GaAs) and gallium
phosphide (GaP), etc). These special type of semiconductor is the cause to produce light.
TYPES OF LEDS
 LEDs are produced in a variety of shapes and size. The color of the plastic lens is often the same as the actual color
of the light emitted.
Traditional inorganic LEDs
Multi color LEDs
Bi-color
Try-color
Organic LED
Miniature
High power
APPLICATION
 Sensor application
 Mobile application
 Sign application
 Automative uses
 LED signals
 Illuminations
 Indicators
LCD
 A liquid crystal display(LCD) is a thin, flat panel display device used for electronically
displaying information such as text, images and moving picture.
 LCD is used in computer monitors,televisions, instrument panels, gaming devices etc…
 Polarization of light is used here to display objects.
How LCDs work ?
 Liquid crystals can adopt a twisted up structure and when we apply electricity to them, they
straighten out again. This is the key how LCD displays turn pixels on and off.
 The polarization property of light is used in LCD screen to switch its colored pixels on or off.
At the back of the back of the screen, there is a bright light that shines out towards the
viewer. In front of this, there are the millions of pixels, each one made up of smaller areas
called sub-pixels, that are colored Red, Green, or Blue.
TYPES OF LCD
 Direct address display
 Passive matrix display
 Active matrix display
Direct address display
 when the display include limited variable
components such as, watches, calculators
 Simple electronics is used to control the components
Passive matrix display
 Each pixel must retain it’s state without a steady electric charge
 Scanned one pixel at a time
 Poor contrast and very slow response times
Active matrix display
 Electric charged is stored between refreshes
 Scanned one row at a time
ADVANTAGES AND DISADVANTAGES
Advantages
 LCDs are highly efficient in terms of power consumption.
 LCDs are relatively cheaper than other displays.
 LCDs are lighter and thinner than cathode-ray tube.
 LCDs provide one of the best contrasts in picture quality.
Disadvantages
 LCDs require an additional light source.
 LCD’s range of temperature is very limited.
 LCDs are slower and less reliable.
•LCDs are used in a wide range of applications, including LCD televisions, computer monitors, instrument panels,
aircraft cockpit displays, and indoor and outdoor signage. ... LCD screens are also used on consumer electronics
products such as DVD players, video game devices and clocks.
8085 PROGRAM FOR BINARY DIVISION
 The 8085 has no division operation. To get the result of the division, we should use the repetitive
subtraction method.
 By using this program, we will get the quotient and the remainder.
 We are saving the data at location 2051H and 2050H.
FLOW DIAGRAM
PROGRAM
 LXI H - Load eXtended Immediate
 MOV B,M - an instruction where the 8-bit data content of the memory
location as pointed by H register pair will be moved to the register B
 MVI C,00 - load a register with an 8-bitsor 1-Bytevalue
 INX - increase the value of the location being pointed by whole HL pair by 1
 JMP - Jump to the address specified
 CMP B - Compare the contents of the register or memory location to the
contents of the accumulator
 JC - Go to the address specified if the Carry flag is set
 SUB B - Sub the contents of B from the Accumulator
 INR - Increment/decrement the contents of the memory location in place
 STA - STore Accumulator contents in memory
 HLT - Stop executing the program
The result is storing at location 3051H and 3050H.
R-2R LADDER DAC
R-2R LADDER DAC
The binary-weighted DAC is appropriate for DAC with
low resolving power. This is because it requires a wide
range of precise resistors to perform error-free operations
for high-order DACs. It is impossible to maintain the
accuracy of the weighted DACs and is expensive. This
leads to the R-2R ladder technique that implements only
two resistors for DAC functionality for every digital bit.
 R-2R configuration is a simple arrangement that consists
of parallel and series resistors connected in the cascaded
form to an operational amplifier. An Operational
amplifier can be used in inverting or non-inverting form
depending on the polarity of output voltage that we want
to get from DAC. R-2R Ladder resistors act as voltage
dividers along with the entire network with the output
voltage dependent on the input voltages.
R-2R LADDER DAC
ARRANGEMENT OF R-2R DAC
The ladder arrangement consists of two resistors
i.e. a base resistor R and a 2R resistor which is
twice the value of the base resistor. This feature
helps to maintain a precise output analog signal
without using a wide range of resistor values.
The R-2R resistor ladder based digital-to-analog
converter (DAC) is a simple, effective, accurate
and inexpensive way to create analog voltages
from digital values.
 This is the most popular DAC. It uses a ladder network
containing series-parallel combinations of two resistors
of values R and 2R. Hence the name.
 The operational amplifier configured as voltage follower
is used to prevent loading. Figure shows the circuit
diagram of a R-2R ladder type DAC having a 4-bit
digital input.
 When a digital signal D3D2D1D0 is applied at the input
terminals of the DAC, an equivalent analog signal is
produced at the output terminal.
R-2R LADDER DAC ANALYSIS WITH THEVENIN THEOREM
 The circuit is simplified to obtain the voltage contribution of each
bit. It can be accomplished using Thevenin’s theorem.
 Thevenin’s theorem is a technique through which we can obtain an
equivalent circuit of the concerned resistance network. A Thevenin
circuit consists of a Thevenin resistance and a Thevenin voltage
that can be replaced in the circuit and work the same as the
original resistance network.
4 BIT R-2R RESISTIVE LADDER NETWORK
 This 4-bit resistive ladder circuit may look complicated, but its all
about connecting resistors together in parallel and series
combinations and working back to the input source using simple
circuit laws to find the proportional value of the output. Lets
assume all the binary inputs are grounded at 0 volts, that is: VA =
VB = VC = VD = 0V (LOW). The binary code corresponding to
these four inputs will therefore be: 0000.
 Starting from the left hand side and using the simplified equation
for two parallel resistors and series resistors, we can find the
equivalent resistance of the ladder network as:
 Resistors R1 and R2 are in “parallel” with each other but in “series”
with resistor R3. Then we can find the equivalent resistance of these
three resistors and call it RA for simplicity (or any other form of
identification you want)
 Then RA is equivalent to “2R”. Now we can see that the equivalent
resistance “RA” is in parallel with R4 with the parallel combination
in series with R5.
 Again we can find the equivalent resistance of this combination
and call it RB.
 So RB combination is equivalent to “2R”. Hopefully we can see
that this equivalent resistance RB is in parallel with R6 with the
parallel combination in series with R7 as shown.
 As before we find the equivalent resistance and call it
RC.
 Again, resistor combination RC is equivalent to “2R”
which is in parallel with R8 as shown.
 As we have shown above, when two equal resistor values are
paralled together, the resulting value is one-half, so 2R in parallel
with 2R equals an equivalent resistance of R.
 So the whole 4-bit R-2R resistive ladder network comprising of
individual resistors connected together in parallel and series
combinations has an equivalent resistance (REQ) of “R” when a
binary code of “0000” is applied to its four inputs.
 Therefore with a binary code of “0000” applied as inputs
GENERALISED R-2R DAC EQUATION
 Where: “n” represents the number of digital inputs within the R-
2R resistive ladder network of the DAC producing a resolution
of: VLSB = VIN/2n.
 Clearly then input bit VA when HIGH will cause the smallest
change in the output voltage, while input bit VD when HIGH will
cause the greatest change in the output voltage. The expected
output voltage is therefore calculated by summing the effect of all
the individual input bits which are connected HIGH.
THANK YOU

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SEMINAR.pptx

  • 1. SEMINAR TOPIC: R-2R LADDER DAC, Photo Electric Devices LED, LCD, Photo diode, Expalin the 8085 pgm for binary division. PRESENTED BY , SARAMBA KRISHNAN C.P SHERUN ANEEV T.P SHIBIN RAJ .A SHONE JOHNSON
  • 2. PHOTO ELECTRICAL DEVICES Devices which give an electrical signal in response to visible, infrared, or ultraviolet radiation
  • 3.  A photoelectric cell, also called sometimes a phototube, electron tube, or electric eye, is an electronic device that is sensitive to incident radiation, especially visible light, which is used to generate or control an output of electric current.  During the latter half of the nineteenth century, many scientists and engineers were simultaneously observing a strange phenomenon: electrical devices constructed from certain metals seemed to conduct electricity more efficiently in the daytime than at night.  This phenomenon, called the photoelectric effect, had been noted years earlier by French physicist Alexandre-Edmond Becquerel (1820–1891), who had invented a very primitive device for measuring the intensity of light by measuring the electrical current produced by photochemical reactions.
  • 4.  The devices, often called photoelectric cells, have the ability to convert light signals into corresponding electric signals. The latter can then be processed by conventional electronic equipment to produce desired results. Photoelectric cells can do more than merely replace the human eye.  The photoelectric cells, have the ability to convert light signals into corresponding electric signals. Photoelectric devices may be classified according to the mechanism of their operation.
  • 5.  The photoelectric effect is the process in which electromaganetic radiation such as visible light, x rays, or gamma rays strike matter and cause an electron to be ejected. The ejected electron is called a photoelectron.  At the time that Becquerel was performing his experiments, it was becoming evident that one metal in particular—selenium—was far more reactive when exposed to light than any other substance. Using selenium as a base, several scientists set out to develop a practical device for measuring light intensity.
  • 6. PHOTOELECTRIC EFFECT  Electrical devices constructed from certain metals seemed to conduct electricity more efficiently in the daytime than at night. This phenomenon, called the photoelectric effect.  The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material
  • 7. USES  Photoelectric cells are used as switches (electric eyes), light detectors (burglar alarms), devices to measure light intensity (light meters), and power sources (solar cells).
  • 8. PHOTO DIODE  Photodiode is a semiconductor p–n junction device that converts light into an electrical current.  The current is generated when photons are absorbed in the photodiode.  Photodiodes may contain optical filters, built-in lenses, and may have large or small surface areas. Photodiodes usually have a slower response time as their surface area increases.  The common, traditional solar cell used to generate electric solar power is a large area photodiode.
  • 10.  Type : -Passive  Working principle :-Converts light into current  Pin configuration :-anode and cathode  Electronic symbol :-
  • 11.  Photodiodes are similar to regular semiconductor diodes except that they may be either exposed (to detect vacuum UV or X-rays) or packaged with a window or optical fiber connection to allow light to reach the sensitive part of the device.  Many diodes designed for use specially as a photodiode use a PIN junction rather than a p–n junction, to increase the speed of response.  A photodiode is designed to operate in reverse bias.
  • 12. OPERATION  A photodiode is a PIN structure or p–n junction. When a photon of sufficient energy strikes the diode, it creates an electron–hole pair. This mechanism is also known as the inner photoelectric effect.  Thus holes move toward the anode, and electrons toward the cathode, and a photocurrent is produced. The total current through the photodiode is the sum of the dark current and the photocurrent, so the dark current must be minimized to maximize the sensitivity of the device.  DARK CURRENT: current that is generated in the absence of light
  • 13.
  • 14. MATERIALS USED TO MAKE A PHOTO DIODE  Material Silicon Germanium Indium gallium arsenide Lead(II) sulfide Mercury cadmium telluride Electromagnetic spectrum wavelength range (nm) 190–1100 400–1700 800–2600 <1000–3500 400–14000
  • 15. Only photons with sufficient energy to excite electrons across the material’s bandgap will produce significant photocurrents. Because of their greater bandgap, silicon-based photodiodes generate less noise than germanium-based photodiodes Binary materials, such as MoS2, and graphene emerged as new materials for the production of photodiodes.
  • 16. FEATURES RESPONSE OF A SILICON PHOTO DIODE VS WAVELENGTH OF THE INCIDENT LIGHT
  • 17. Spectral responsivity:- The spectral responsivity is a ratio of the generated photocurrent to incident light power, expressed in A/W when used in photoconductive mode Dark current:- The dark current is the current through the photodiode in the absence of light, when it is operated in photoconductive mode. Response time:- The response time is the time required for the detector to respond to an optical input Noise-equivalent power:- Noise-equivalent power (NEP) is the minimum input optical power to generate photocurrent, equal to the rms noise current in a 1 hertz bandwidth
  • 18. APPLICATION  Photodiodes are often used for accurate measurement of light intensity in science and industry.  Used as photoconductors, charge-coupled devices (CCD), and photomultiplier tubes  Devices such as compact disc players, smoke detectors, medical devices  Accurate measurement of light intensity in science and industry  Various medical applications, such as detectors for computed tomography , instruments to analyze samples (immunoassay), and pulse oximeters.
  • 19. LED & LCD LED: In the simplest terms, a light-emitting diode (LED) is a semiconductor device that emits light when an electric current is passed through it. Light is produced when the particles that carry the current (known as electrons and holes) combine together within the semiconductor material LCD : In the simplest terms, A liquid crystal display(LCD) is thin, flat panel display device used for electronically displaying information such as text, images and moving picture.
  • 20. LED  A light emitting diode(LED) is essentially a PN junction opto semiconductor that emits a monochromatic (single color) light when operated in a forward biased direction.  LEDs convert electrical energy into light energy. How does a LED work ?  Light is a form of energy that is released from atoms. Light consists of many small energy packets that have momentum but no mass. In the atom, electrons move in orbit around the nucleus, and the electrons in different orbits have different amounts of energy. When electrons descend from a higher orbit to a lower one energy is released in the form of photons.  The same thing happens inside the LED. Actually, an LED is a type of PN-junction diode that uses a special type of semiconductor (such as gallium arsenide (GaAs) and gallium phosphide (GaP), etc). These special type of semiconductor is the cause to produce light.
  • 21. TYPES OF LEDS  LEDs are produced in a variety of shapes and size. The color of the plastic lens is often the same as the actual color of the light emitted. Traditional inorganic LEDs Multi color LEDs Bi-color Try-color Organic LED Miniature High power APPLICATION  Sensor application  Mobile application  Sign application  Automative uses  LED signals  Illuminations  Indicators
  • 22. LCD  A liquid crystal display(LCD) is a thin, flat panel display device used for electronically displaying information such as text, images and moving picture.  LCD is used in computer monitors,televisions, instrument panels, gaming devices etc…  Polarization of light is used here to display objects. How LCDs work ?  Liquid crystals can adopt a twisted up structure and when we apply electricity to them, they straighten out again. This is the key how LCD displays turn pixels on and off.  The polarization property of light is used in LCD screen to switch its colored pixels on or off. At the back of the back of the screen, there is a bright light that shines out towards the viewer. In front of this, there are the millions of pixels, each one made up of smaller areas called sub-pixels, that are colored Red, Green, or Blue.
  • 23. TYPES OF LCD  Direct address display  Passive matrix display  Active matrix display Direct address display  when the display include limited variable components such as, watches, calculators  Simple electronics is used to control the components Passive matrix display  Each pixel must retain it’s state without a steady electric charge  Scanned one pixel at a time  Poor contrast and very slow response times Active matrix display  Electric charged is stored between refreshes  Scanned one row at a time
  • 24. ADVANTAGES AND DISADVANTAGES Advantages  LCDs are highly efficient in terms of power consumption.  LCDs are relatively cheaper than other displays.  LCDs are lighter and thinner than cathode-ray tube.  LCDs provide one of the best contrasts in picture quality. Disadvantages  LCDs require an additional light source.  LCD’s range of temperature is very limited.  LCDs are slower and less reliable.
  • 25. •LCDs are used in a wide range of applications, including LCD televisions, computer monitors, instrument panels, aircraft cockpit displays, and indoor and outdoor signage. ... LCD screens are also used on consumer electronics products such as DVD players, video game devices and clocks.
  • 26. 8085 PROGRAM FOR BINARY DIVISION
  • 27.  The 8085 has no division operation. To get the result of the division, we should use the repetitive subtraction method.  By using this program, we will get the quotient and the remainder.  We are saving the data at location 2051H and 2050H.
  • 30.  LXI H - Load eXtended Immediate  MOV B,M - an instruction where the 8-bit data content of the memory location as pointed by H register pair will be moved to the register B  MVI C,00 - load a register with an 8-bitsor 1-Bytevalue  INX - increase the value of the location being pointed by whole HL pair by 1  JMP - Jump to the address specified  CMP B - Compare the contents of the register or memory location to the contents of the accumulator  JC - Go to the address specified if the Carry flag is set  SUB B - Sub the contents of B from the Accumulator  INR - Increment/decrement the contents of the memory location in place  STA - STore Accumulator contents in memory  HLT - Stop executing the program
  • 31. The result is storing at location 3051H and 3050H.
  • 33. R-2R LADDER DAC The binary-weighted DAC is appropriate for DAC with low resolving power. This is because it requires a wide range of precise resistors to perform error-free operations for high-order DACs. It is impossible to maintain the accuracy of the weighted DACs and is expensive. This leads to the R-2R ladder technique that implements only two resistors for DAC functionality for every digital bit.
  • 34.  R-2R configuration is a simple arrangement that consists of parallel and series resistors connected in the cascaded form to an operational amplifier. An Operational amplifier can be used in inverting or non-inverting form depending on the polarity of output voltage that we want to get from DAC. R-2R Ladder resistors act as voltage dividers along with the entire network with the output voltage dependent on the input voltages.
  • 36. ARRANGEMENT OF R-2R DAC The ladder arrangement consists of two resistors i.e. a base resistor R and a 2R resistor which is twice the value of the base resistor. This feature helps to maintain a precise output analog signal without using a wide range of resistor values. The R-2R resistor ladder based digital-to-analog converter (DAC) is a simple, effective, accurate and inexpensive way to create analog voltages from digital values.
  • 37.  This is the most popular DAC. It uses a ladder network containing series-parallel combinations of two resistors of values R and 2R. Hence the name.  The operational amplifier configured as voltage follower is used to prevent loading. Figure shows the circuit diagram of a R-2R ladder type DAC having a 4-bit digital input.  When a digital signal D3D2D1D0 is applied at the input terminals of the DAC, an equivalent analog signal is produced at the output terminal.
  • 38. R-2R LADDER DAC ANALYSIS WITH THEVENIN THEOREM  The circuit is simplified to obtain the voltage contribution of each bit. It can be accomplished using Thevenin’s theorem.  Thevenin’s theorem is a technique through which we can obtain an equivalent circuit of the concerned resistance network. A Thevenin circuit consists of a Thevenin resistance and a Thevenin voltage that can be replaced in the circuit and work the same as the original resistance network.
  • 39. 4 BIT R-2R RESISTIVE LADDER NETWORK  This 4-bit resistive ladder circuit may look complicated, but its all about connecting resistors together in parallel and series combinations and working back to the input source using simple circuit laws to find the proportional value of the output. Lets assume all the binary inputs are grounded at 0 volts, that is: VA = VB = VC = VD = 0V (LOW). The binary code corresponding to these four inputs will therefore be: 0000.  Starting from the left hand side and using the simplified equation for two parallel resistors and series resistors, we can find the equivalent resistance of the ladder network as:
  • 40.  Resistors R1 and R2 are in “parallel” with each other but in “series” with resistor R3. Then we can find the equivalent resistance of these three resistors and call it RA for simplicity (or any other form of identification you want)  Then RA is equivalent to “2R”. Now we can see that the equivalent resistance “RA” is in parallel with R4 with the parallel combination in series with R5.
  • 41.  Again we can find the equivalent resistance of this combination and call it RB.  So RB combination is equivalent to “2R”. Hopefully we can see that this equivalent resistance RB is in parallel with R6 with the parallel combination in series with R7 as shown.
  • 42.  As before we find the equivalent resistance and call it RC.  Again, resistor combination RC is equivalent to “2R” which is in parallel with R8 as shown.
  • 43.  As we have shown above, when two equal resistor values are paralled together, the resulting value is one-half, so 2R in parallel with 2R equals an equivalent resistance of R.  So the whole 4-bit R-2R resistive ladder network comprising of individual resistors connected together in parallel and series combinations has an equivalent resistance (REQ) of “R” when a binary code of “0000” is applied to its four inputs.  Therefore with a binary code of “0000” applied as inputs
  • 44. GENERALISED R-2R DAC EQUATION  Where: “n” represents the number of digital inputs within the R- 2R resistive ladder network of the DAC producing a resolution of: VLSB = VIN/2n.  Clearly then input bit VA when HIGH will cause the smallest change in the output voltage, while input bit VD when HIGH will cause the greatest change in the output voltage. The expected output voltage is therefore calculated by summing the effect of all the individual input bits which are connected HIGH.