DAC, Diodes, and Triacs

Siri BeltonJeremy Hill

and Brandon Whitt

Outline• What is DAC?• Applications• Types of DAC

– Binary Weighted Resistor– R-2R

• Specifications– Reference Voltage– Resolution– Sampling Rate– Settling Time– Linearity– Errors

• Diodes– Overview– Real v. Ideal– Types: Zener, LED

• Triacs

What is DAC?

• Device that converts digital numbers into an analog output.

• Output can be a voltage or a current

0101

0011

0111

1001

1001

1010

1011 DAC

Siri Belton

What is DAC?

• Each binary number corresponds to a specific voltage output

Siri Belton

Reference Voltage• Use input reference voltages to determine the

analog output.• Output voltage, unipolar 0 to Vref

• Output voltage, bipolar -Vref to Vref

Analog Reference Voltage (Vref)

Analog Output (Vout)

Digital to Analog

Converter

N-Bit Binary Word

Siri Belton

Applications

• Used anywhere a digital signal is used to create an analog output

• Audio/Video– CDs, Cell Phones, Speakers, DVDs, Youtube

• Signal Generator

Siri Belton

Types of DAC

• Binary-weighted resistor• R-2R ladder• Pulse width modulation• Oversampling (Delta Sigma)• Cyclic• Hybrid DAC

Siri Belton

Binary-Weighted Resistors

• Adds resistors in parallel to divide voltage on each branch by a power of two

• Transistors act as switches

Siri Belton

Binary-Weighted ResistorsEquivalent Circuit:

A

B

C

D

Where A, B, C, and D are 1 or 0

Siri Belton

Binary-Weighted Resistors

• Advantages:– Useful for conversions up to 8-bit– Simple– Fast

• Disadvantages– Need large range of resistor values (2048:1 for a 12-bit

conversion) with high precision resistor values– Need small switch resistances– Op-amp can have trouble producing low currents at the

lower range of a high precision DAC

Siri Belton

Siri Belton

• Each bit controls the switch to the op-amp or ground (grounded if zero)

𝑉 𝑟𝑒𝑓

R-2R Ladder

𝑅 𝑓

R-2R LadderSiri Belton

𝑅𝑒𝑞=1

12𝑅 +

12𝑅

=𝑅

𝑉 𝑟𝑒𝑓

0 1 112

RV V VR R

1 2 212

RV V VR R

2 3 312

RV V VR R

𝑅 𝑓

R-2R Ladder

• Advantages– Need only 2 resistor values– Lower precision is acceptable

• Disadvantages– Slower conversion rate

Siri Belton

Specifications of a DAC

• Reference Voltage• Resolution• Sampling Rate• Settling Time• Linearity• Errors

Jeremy Hill

Reference Voltage (Vref)

• The reference voltage determines the output voltage range.

• For Non-multiplying DAC:– Vref is set internally by the manufacturer– Constant Value

• For Multiplying DAC:– Vref is set externally– Can be varied during operation

• Full Scale Voltage (Vfs)– Voltage when all digital inputs are 1’s

N

NVV2

)12(reffs

Jeremy Hill

Resolution

• Resolution is the amount of output voltage change in response to a least significant bit (LSB) transition.

• Smaller resolution results in a smoother output• A common DAC has a 8-16 bit resolution

LSBref

2Resolution VV

N

Jeremy Hill

Sampling Rate (fs)

• Sampling rate is the rate at which the DAC can convert the digital input to an output voltage

• The Nyquist Criterion is used to ensure the output correctly represents the digital input

• fmax is the max frequency of the analog signal to be reconstructed

• fs is limited by the clock speed of the input signal and the settling time of the DAC

maxsampling 2 ff

Jeremy Hill

Settling Time

• DAC needs time to reach the actual expected analog output voltage– The time required for the output voltage to settle

within +/- ½ of VLSB of the expected voltage

Jeremy Hill

Linearity

• The difference between the desired analog output and the actual output over the full range of expected values

010101000011001000010000Digital Input Signal

Ana

log

Out

put S

igna

l

010101000011001000010000 010101000011001000010000Digital Input Signal

Ana

log

Out

put S

igna

l

010101000011001000010000Digital Input Signal

Ana

log

Out

put S

igna

l

010101000011001000010000 010101000011001000010000Digital Input Signal

Ana

log

Out

put S

igna

l

Linear (Ideal) Non-Linear

Jeremy Hill

Errors

• Gain Error• Offset Error• Full Scale Error• Non Linearity• Non-Monotonic• Resolution Errors• Settling Time and Overshoot

Jeremy Hill

Gain Error

• Deviation in the slope of the actual transfer function from the ideal transfer function– Can be determined by measuring the output

voltage for a digital input of all 1’s

Jeremy Hill

Offset Error

• Occurs when there is an offset in the actual output voltage from the ideal output– Can be determined by measuring the output

voltage for a digital input of zero

Jeremy Hill

Full Scale Error

• Combination of gain and offset error

Jeremy Hill

Differential Non-Linearity (DNL)

• The difference between two successive digital output codes is ideally 1 VLSB

• DNL error is the deviation from a step of 1 VLSB

• Manufacturers will specify a maximum DNL error

Jeremy Hill

Integral Non-Linearity (INL)

• The difference in the ideal linear voltage and the actual output voltage for a given digital code– Manufacturers will specify the max INL error

Jeremy Hill

Non-Monotonic

• Occurs when an increase in digital input results in a lower output voltage– If the DNL error is less than +/- 1 LSB the DAC is

guaranteed to be monotonic

Jeremy Hill

Resolution Errors

• Resolution will determine how close the output voltage matches the desired signal

1 Bit Resolution 3 Bit Resolution

Jeremy Hill

Settling Time and Overshoot

• Any change in the input time will not be reflected immediately due to the lag time

• Overshoot occurs when the output voltage overshoots the desired analog output voltage

Jeremy Hill

DiodesWhat are they?

• A diode is a two terminal electric component which conducts current more easily in one direction than in the opposite direction.

• The most common usage of a diode is as an electronic valve which allows current to flow in one direction but not the opposite direction.

Brandon Whitt

DiodesHow do they work?

• A diode is created when a p-type semiconductor is joined with and n-type semiconductor.

• At the boundary a depletion region will form within the diode. Here the p-carriers will diffuse into the n-type region and vice versa.

np

Depletion Region

Majority carriers

Brandon Whitt

DiodesReal vs Ideal

V

I

conductionregion

non-conductionregion

Ideal Curve

Ideal Diode – no resistance to current flowin the forward direction and infinite resistancein the reverse direction.

Brandon Whitt

Zener Diode

• Every p-n junction (i.e. diode) will break down in reverse bias if enough voltage is applied. Zener diodes are designed to operate in this breakdown region.

• Zener diodes have a specified voltage drop when they are used in reverse bias. They are able to maintain a nearly constant voltage under conditions of widely varying current.

Brandon Whitt

Other Diodes• Light Emitting Diodes (LEDs):

Photons are emitted when the carriers pass through the junction and recombine with the doped region.

• Photodiode: Photons hitting the doped regions cause charged carriers to form. These can be used to sense light in and Opto-isolator.

Brandon Whitt

TRIACTriode for AC current

• The TRIAC is an electronic component that can allow current to flow in EITHER direction when triggered (bidirectional).

• TRIACs make good switches for AC current.• They can handle hundreds of amps and

thousands of watts of power.

Brandon Whitt

TRIACsThey’re made of smaller components

• TRIACs are composed of Transistors and Thyristors.• Two Transistors (PNP and NPN back-to-back) are combined to

make a Thyristor. Current can only go one direction (Unidirectional).

• With forward voltage, small gate current pulse turns on the device. Once on, each transistor supplies gate current for the other so the device stays on.

Brandon Whitt

TRIACsThey’re made from two Thyristors

• A TRIAC is a 3-terminal switch composed of 2 thyristors facing opposite directions

• It can conduct current bidirectionally• MT1 and MT2 are current carrying

terminals while the Gate terminal is used for triggering by applying a small voltage signal.

• Once triggered, it continues to conduct current until the current falls below a threshold – known as holding current

Brandon Whitt

TRIACsCircuit Example

• Simple Triac Switch

• Small control current/voltage

• Eliminates Mechanical wear in a Relay

• Much Cheaper

Brandon Whitt

TRIACsSummary

• TRIACs start conducting when a minimum current (gate threshold current) flows into or out of its gate sufficient to turn on relevant junctions in that quadrant of operation

• Device remains in “on” state even after gate current is removed so long as current through the device remains above holding current

• Once current falls below holding current for an appropriate time period, device switches “off”

Brandon Whitt

TRIACsPros and Cons

Pros:• Can handle much more current than a

transistor• Much cheaper than relaysCons:• Can not stop the current from flowing by using

the gate. The current must be stopped at the terminal.

Brandon Whitt

TRIACsApplications

High Power: Switches in AC circuits using milliamp control currents to turn on kilowatt power flows.

Low Power: Dimmers for light bulbs, speed controls for electric fan motors, control circuits in appliances

Specs to consider when purchasing a TRIAC:• Gate signal requirements• Voltage drop• Steady-state/holding/peak current specifications

Brandon Whitt