Sensors

Read Chapter 2 of Textbook

1. Displacement Sensors

• Potentiometer (Already discussed)

• Strain Gages

• Inductive Sensors (LVDT)

• Capacitive Sensors

• Piezoelectric Sensors

=(A/V)/m = S/m

P and N doped Silicon Strain GagesGage Factor = G = (ΔR/R)/(ΔL/L)

---Stretching bar of N-type silicon crystal breaks electrons loose from impurity sites, making resistance decrease, producing large negative G.

---Stretching bar of P-type silicon crystal inhibits holes from moving away from their impurity sites, producing large positive G

Unbonded Strain Gage Pressure Sensor

This is a deflection mode instrument, so it is important to choose

Ri >> R1=R2=R3=R4

To avoid bridge loading

D.

BONDED Strain Gages

Silicon Integrated Circuit Pressure Sensor

Inductive Transducers

<- L <- L+Vo(t)-

Coils must be wound in opposite directions so magnetic fluxes oppose

µ = magnetic permeability of core material = µ R4π*10-7 F/m

Linear Variable Differential Transformer Displacement Transducer

LVDT used to measure very small displacements in a seismometer that measures movements in the earth’s crust due to earthquakes. It consists of a middle primary coil and two outer secondary coil. The magnetic core moves freely without touching bobbins, and at the null (zero) position, it extends halfway into each secondary coil.

Example Medical Applications of Linear Variable Displacement Transformer (LVDT)

NOTE: The output voltage is actually the PEAK voltage of an ac sine wave whose frequency is that of the primary winding excitation sine wave.

Advantages of LVDTs as displacement sensors

Disadvantages of LVDTs• All these advantages, in addition to their

reasonable cost, have made the LVDT an attractive displacement measurement sensor. However, LVDTs for use in medical applications have the following disadvantages: – They require a high frequency, constant-amplitude ac

sinusoidal excitation.– They cannot be used in the vicinity of equipment that

creates strong magnetic fields.– A somewhat complicated “phase sensitive” ac-to-dc

converter (detector) must be used if both positive and negative displacements from the middle (null) position needs to be measured.

LVDT showing AC Excitation and Phase Sensitive Demodulator

Phase INSENSITIVE Detector (Diode Half-wave rectifier with capacitive filter.)

Commercial Diode Ring Modulator (also called “Double Balanced Mixer”

LVDT Detector Circuit without need for a Phase-Sensitive Demodulator

LVDT Excitation Circuit (Power oscillator (1 kHz Power Sine Wave Oscillator)

ic(t)

Does not effect circuit, since output resistance of op amp is nearly 0 ohms

C = q/v => v = q/C => kfL/(ε0εRA)L = thicknessof piezo transducer

Molecular Model of a Simple Piezoelectric Material: ZnS

How is the piezoelectric constant “k” (recall q = kF) related the constant “K” above? Recall the definition of Young’s Modulus, Y:

Lx

AfY

/

/ => x

L

YAf

xKxL

YAkfkq

Therefore where

L

YAkK

A

f

L

x

Rs Cs Cc Ca

q = Kx

is = dq/dt = Kdx/dt

Crystal Amplifier

Cable

Ra

CaCcCsC

RaRsR

//

dt

dvCi

vCq

C0

0

iSiRiC

dt

dvCi

vCq

C0

0

Eqn 2.19 is now written in phasor form:

XRCjC

KjVo

R

VoXjKVojC

)1(

This transfer function is of the same form as that of the RC HPF 1st order filter and also the capacitive displacement sensor.

So, like the capacitive transducer, it cannot transduce constant (dc) displacements!

-

+3

21

84

R1

10k

R2

11.1k

VCC = 15 V

VEE = -15 V

C2

160 nF

C1

1uFPiezoXducer

R3

3.2MEG

Vout

100 kΩ and

100k Ω) = 16 nF

16 nF

100k

Piezoelectric Displacement Sensor has a high pass filter step response

xo C

Kx0

Predicting Piezo Transducer Step Response Via Laplace Transforms

/)(

11)(

1)(

1)(

)()(

tSo

SooSS

S

eKxtvo

s

Kx

s

x

s

sKsX

s

sKsVo

s

sK

sX

sVosH

Replacing “jω” in Text Eqn 2.20 by the Laplace complex frequency variable “s”

x(t)

vo(t)

t = 0

0

xo

xoKS

t = τ = RC

xoKSe-1 = 0.37xoKS

- xoKS

Note that for a step input of amplitude xo, x(t) = xo u(t) => X(s) = x0/s

Note this is response only to the leading edge of the input pulse, x(t) = x0 u(t)

But in reality, x(t) = x0 {u(t) – u(t-Td)}

t=Td

Useable Operating Frequency Range

for “wideband” signal transducer,

such as audio microphone

Operating frequency for very sensitive, narrow-band signal transducer,

such as 40 kHz resonant ultrasonic pulsed

distance measuring application

+

vout

-

1. Magnitude of voltage gain around feedback loop “BA” must be > 1 at frequency of oscillation.

2. Phase shift around feedback loop must be an integer multiple of 360 degrees so oscillations can build up at frequency of oscillation.

General Block Diagram of a Feedback Oscillator

Biasing Resistor R1R1 acts as a feedback resistor, biasing the inverter into its linear amplifying region of operation, and effectively causing it to function as a high gain inverting amplifier. To see this, assume the inverter is ideal, with very high input impedance and very low output resistance; this resistor forces the inverter’s input and output voltages to be equal. Hence the inverter will neither be fully on nor off, but in the transition region where it has gain.Piezoelectric Crystal ResonatorThe crystal in combination with C1 and C2 forms a Hi-Q “Pi network” bandpass filter, which provides a 180 degree phase shift and also a voltage gain from the output to input at approximately the resonant frequency of the crystal. To understand the operation of this, it can be noted that at the frequency of oscillation, the crystal appears inductive; thus it can be considered a large inductor with a very high Q. The combination of the 180 degree phase shift (i.e. inverting gain) from the pi network and the negative gain from the inverter results in a positive loop gain, making the bias point set by R1 unstable and leading to oscillation.

Vi Vo

Vo

Vi

Vo=ViLoad line

established by biasing

resistor R1, biases inverter into its analog

amplifying region

Pierce Crystal Oscillator Circuit Made from Digital Inverter Gate

8 MHz Crystal OscillatorRFC (RF Choke) is a 10 uH inductor that has a high enough reactance at the parallel resonant frequency of the XTAL (8 MHz) to guarantee a loop gain > 1 at 8 MHz. Note XRFC = 500 ohms at 8 MHz. Oscillator will have high harmonic content with RFC, so RFC is sometimes replaced with parallel resonant circuit to encourage oscillation at only the harmonic frequency the parallel resonant circuit has been tuned to resonate at.

R1, R2, RE bias BJT CE amplifier into the middle of its amplifying region.

Typical Values:Vcc = 9 V, R1 = R2 = 560 ohms, RE = 1 k ohm, Cb = 0.1 uFC1 = C2 = 30 pF (XTAL often cut to resonate at desired frequency with these external values of C1 and C2.)

How DLP Technology Works1. The semiconductor that continues to reinvent projectionAt the heart of every DLP® projection system is an optical semiconductor known as the DLP® chip, which was invented by Dr. Larry Hornbeck of Texas Instruments in 1987.The DLP chip is perhaps the world's most sophisticated light switch. It contains a rectangular array of up to 2 million hinge-mounted microscopic mirrors; each of these micromirrors measures less than one-fifth the width of a human hair.When a DLP chip is coordinated with a digital video or graphic signal, a light source, and a projection lens, its mirrors can reflect a digital image onto a screen or other surface. The DLP chip combined with the advanced electronics that surround it produce stunning images and video that have redefined picture quality.

DLP (Digital Light Processor ) IC

2. The grayscale imageA DLP chip's micromirrors tilt either toward the light source in a DLP projection system (ON) or away from it (OFF). This creates a light or dark pixel on the projection surface.The bit-streamed image code entering the semiconductor directseach mirror to switch on and off up to several thousand times per second. When a mirror is switched on more frequently than off, it reflects a light gray pixel; a mirror that's switched off more frequently reflects a darker gray pixel.In this way, the mirrors in a DLP projection system can reflect pixels in up to 1,024 shades of gray to convert the video or graphic signal entering the DLP chip into a highly detailed grayscale image.

3. Adding colorThe white light generated by the lamp in a DLP projection system passes through a color filter as it travels to the surface of the DLP chip. This filters the light into a minimum of red, green, and blue, from which a single-chip DLP projection system can create at least 16.7 million colors.

With BrilliantColor™ Technology, additional colors are added including Cyan, Magenta and Yellow to expand the color pallet for even more vibrant color performance.

Some DLP projectors offer solid-state illumination which replaces the traditional white lamp. As a result, the light source emits the necessary colors eliminating the color filter.

In some DLP systems, a 3-chip architecture is used, particularly for high brightness projectors required for large venue applications such as concerts and movie theaters. These systems are capable of producing no fewer than 35 trillion colors.

The on and off states of each micromirror are coordinated with these basic building blocks of color. For example, a mirror responsible for projecting a purple pixel will only reflect red and blue light to the projection surface; those colors are then blended to see the intended hue in a projected image.

Many data projectors and HDTVS using DLP technology rely on a single chip configuration like the one described above.

White light passes through a color filter, causing red, green, blue and even additional primary colors such as yellow cyan, magenta and more to be shone in sequence on the surface of the DLP chip.

The switching of the mirrors, and the proportion of time they are 'on' or 'off' is coordinated according to the color shining on them. Then the sequential colors blend to create a full-color image you see on the screen.

“Single Chip” DLP Technology

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