electronic instrumentation 1 experiment 10 analog vs. digital circuits comparators and schmitt...

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Electronic InstrumentationExperiment 10

• Analog vs. Digital Circuits

• Comparators and Schmitt Triggers• Combinational Logic Devices• Sequential Logic Devices• Bipolar Junction Transistors• Inside the 555 Timer

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12 April 2004 Electronic Instrumentation 2

Analog Circuits vs. Digital Circuits

An analog signal is an electric signal whose value varies continuously over time.

A digital signal can take on only finite values as the input varies over time.


• A binary signal, the most common digital signal, is a signal that can take only one of two discrete values and is therefore characterized by transitions between two states.

• In binary arithmetic, the two discrete values f1 and f0 are represented by the numbers 1 and 0, respectively.


• In binary voltage waveforms, these values are represented by two voltage levels.

• In TTL convention, these values are nominally 5V and 0V, respectively.

• Note that in a binary waveform, knowledge of the transition between one state and another is equivalent to knowledge of the state. Thus, digital logic circuits can operate by detecting transitions between voltage levels. The transitions are called edges and can be positive (f0 to f1) or negative (f1 to f0).

0

1positiveedge

positiveedge

negativeedges


Comparators and Schmitt Triggers• In this section we will use op-amps to

create binary signals.• Comparators are the simplest way to

create a binary signal with an op amp. They take advantage of the very high gain of the chip to force it to saturate either high (VS

+) or low (VS-) creating

two (binary) states.• Schmitt Triggers are a modified

version of a comparator which uses a voltage divider to improve the performance of the comparator in the presence of noise.


Op-Amp Comparator• The prototype of op-amp switching circuits is the

op-amp comparator.• The circuit does not employ feedback.

outV A V V


• Because of the large gain that characterizes open-loop performance of the op-amp (A > 105), any small difference between the input voltages will cause large outputs; the op-amp will go into saturation at either extreme, according the voltage supply values and the polarity of the voltage difference.

• One can take advantage of this property to generate switching waveforms.

• Consider the following.

V cos t Non-inverting Op-Amp Comparator


• The comparator is perhaps the simplest form of an analog-to-digital converter, i.e., a circuit that converts a continuous waveform to discrete values. The comparator output consists of only two discrete levels.

V = 1 volt

Vsat = ± 13.5 volts

Input and Output of Non-Inverting Comparator


• It is possible to construct an inverting comparator by connecting the non-inverting terminal to ground and connecting the input to the inverting terminal.

Input and Output of Inverting Comparator


• Comparator with Offset• A simple modification of the comparator circuit

consists of connecting a fixed reference voltage to one of the input terminals; the effect of the reference voltage is to raise or lower the voltage level at which the comparator will switch from one extreme to the other.


• Below is the waveform of a comparator with a reference voltage of 0.6 V and an input voltage of sin(ωt).

• Note that the comparator output is no longer a symmetric square wave.


• Another useful interpretation of the op-amp comparator can be obtained by considering its input-output transfer characteristic.

Non-Inverting Zero-Reference(no offset) Comparator

often called azero-crossing comparator


• Shown below is the transfer characteristic for a comparator of the inverting type with a nonzero reference voltage.


Comparator Response to Noisy Inputs

Note how the output swings between high and low.


Schmitt Trigger• One very effective way of

improving the performance of the comparator is by introducing positive feedback. Positive feedback can increase the switching speed of the comparator and provide noise immunity at the same time.

• The voltage range over which the signal does not switch is called the hysteresis (In this case, h=2d) Can you explain how this works?


• In effect, the Schmitt trigger provides a noise rejection range equal to ± Vsat [R2 / (R2 + R1)] within which the comparator cannot switch.

• Thus if the noise amplitude is contained within this range, the Schmitt trigger will prevent multiple triggering.


• If it is desired to switch about a voltage other than zero, a reference voltage can also be connected to the non-inverting terminal. In this case, d+ is not equal to d-, and the hysteresis is given by h=d+ + d-

Switching levels for the Schmitt Trigger are:

2 1in sat ref

2 1 2 1

R RV V V

R R R R

positive-going transition

2 1in sat ref

2 1 2 1

R RV V V

R R R R

negative-going transition


Combinational Logic Devices Logic Gates perform basic logic operations, such as

AND, OR and NOT, on binary signals. In this class, we use them as black boxes. This means

that we do not worry about how these chips are built inside, but only about what output they produce for all possible inputs.

In order to show this behavior, we use truth tables, which show the output for all input combinations.

The outputs of combinational logic gates depend only on the instantaneous values of the inputs.


Logic Gates


Logic Gate Example: XOR

Input Input Output

A B X

0 0 0

0 1 1

1 0 1

1 1 0

Question: What common household switch configuration corresponds to an XOR?


Boolean Algebra

• The variables in a boolean, or logic, expression can take only one of two values, 0 (false) and 1 (true).

• We can also use logical mathematical expressions to analyze binary operations, as well.


• The basis of boolean algebra lies in the operations of logical addition, or the OR operation, and logical multiplication, or the AND operation.

• OR Gate• If either X or Y is true (1), then Z is true (1)

• AND Gate• If both X and Y are true (1), then Z is true (1)

• Logic gates can have an arbitrary number of inputs.• Note the similarities to the behavior of the mathematical

operators plus and times.


Laws of Boolean Algebra


DeMorgan’s Laws


Using DeMorgan’s Laws

Important Principal based on DeMorgan’s Laws: Any logic function can be implemented by using only OR and NOT gates, or only AND and NOT gates.


Sequential Logic Devices In a sequential logic device, the timing or sequencing

of the input signals is important. Devices in this class include flip-flops and counters.

Positive edge-triggered devices respond to a low-to-high (0 to 1) transition, and negative edge-triggered devices respond to a high-to-low (1 to 0) transition.

0

1positiveedge

positiveedge

negativeedges


Flip-Flops• A flip-flop is a sequential device that can store and

switch between two binary states.

• It is called a bistable device since it has two and only two possible output states: 1 (high) and 0 (low).

• It has the capability of remaining in a particular state (i.e., storing a bit) until the clock signal and certain combinations of the input cause it to change state.


Simple Flip Flop Example: The RS Flip-Flop

Q = 1

Q = 0 Note that the output depends on three things: the two inputs and the previous state of the output.


Inside the R-S Flip Flop

Note that the enable signal is the clock, which regularly pulses. This flip flop changes on the rising edge of the clock. It looks at the two inputs when the clock goes up and sets the outputs according to the truth table for the device.


Inside the J-K Flip Flop

Note this flip flop, although structurally more complicated, behaves almost identically to the R-S flip flop, where J(ump) is like S(et) and K(ill) is like R(eset). The major difference is that the J-K flip flop allows both inputs to be high. In this case, the output switches state or “toggles”.


Binary Counters Binary Counters do exactly what it sounds like they should.

They count in binary. Binary numbers are comprised of only 0’s and 1’s.

Decimal QD QC QB QA

0 0 0 0 0

1 0 0 0 1

2 0 0 1 0

3 0 0 1 1

4 0 1 0 0

5 0 1 0 1


Binary – Decimal -- Hexadecimal Conversion10110101110001011001110011110110 binary number

11 5 12 5 9 12 15 6

B 5 C 5 9 C F 6

equivalent base 10 value for each group of 4 consecutive binary digits (bits)

corresponding hexadecimal (base 16) digit

B5C59CF6equivalent hexadecimal number

Decimal 8 = 1x23 + 0x22 + 0x21 +0x20 = 01000 in Binary

Calculator Applet


Binary Counters are made with Flip Flops

Each flip flop corresponds to one bit in the counter. Hence, this is a four-bit counter.

http://www.play-hookey.com/digital/synchronous_counter.html


Typical Output for Binary Counter

Note how the Q outputs form 4 bit numbers


Bipolar Junction Transistors The bipolar junction transistor

(BJT) is the salient invention that led to the electronic age, integrated circuits, and ultimately the entire digital world. The transistor is the principal active device in electrical circuits.

When inputs are kept relatively small, the transistor serves as an amplifier. When the transistor is overdriven, it acts as a switch, a mode most useful in digital electronics.


A BJT consists of three adjacent regions of doped silicon, each of which is connected to an external lead. The base, a very thin slice of one type, is sandwiched by the complementary pair of the other type, hence the name bipolar.

There are two types of BJTs, npn and pnp, and the three layers are called collector (C), base (B), and emitter (E). C E

B

All current directions are reversed from the npn-type to the pnp-type.

npn transistor


MOSFET

Applying a gate voltage that exceeds the threshold voltage opens up the channel between the source and the drain

This is from an excellent collection of java applets at SUNY Buffalo http://jas.eng.buffalo.edu/

http://jas.eng.buffalo.edu/


VC

VE

VB

IB

IC

IE

++

-

--VCE

-VBE

VC

VE

VB

IB

IC

IE

+

+ --

VCE

VBE

CE C E

BE B E

E C B

V V V

V V V

I I I

npn BJTpnp BJT

VCE > 0VBE > 0

VCE < 0VBE < 0

Apply voltage HIGHto base to turn ON

Apply voltage LOWto base to turn ON

pnp and npn transistors Note: The npn-type is the more popular; it is faster and costs less.


Regions of the npn BJT Cutoff Region

• Not enough voltage at B for the diode to turn on.

• No current flows from C to E and the voltage at C is Vcc.

Saturation Region• The voltage at B exceeds 0.7 volts, the diode turns on and the maximum

amount of current flows from C to E.

• The voltage drop from C to E in this region is about 0.2V but we often assume it is zero in this class.

Active Region• As voltage at B increases, the diode begins to turn on and small

amounts of current start to flow through into the doped region. A larger current proportional to IB, flows from C to E.

• As the diode goes from the cutoff region to the saturation region, the voltage from C to E gradually decreases from Vcc to 0.2V.

C BI I 10 1000


Model of the npn BJT The diode is controlled by the

voltage at B. When the diode is completely

on, the switch is closed. This is the saturation region.

When the diode is completely off, the switch is open. This is the cutoff region.

When the diode is in between we are in the active region.


npn Common Emitter Characteristics

IC = βIB

VBE = 0.7 V

VBE < 0.6 V

C

E

C

B

I

I

I

I 1

0.9 0.999

10 1000


Using the transistor as a switch


Building logic gates with transistorsInput Output

0 1

1 0


Inside the 555 Timer animation

+V

-V

-

+

+V

-V

-

+R

S

Q

Q

3

4

1

7

2

6

5

8

R

R

R

Control Flip-FlopTrigger Comparator

Threshold Comparator

Output

ResetVcc

Trigger

Discharge

Control

555 Timer

Threshold

electronic instrumentation 1 experiment 10 analog vs. digital circuits comparators and schmitt...

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