Chem 422 Final -- Chapters 1-5

What can an instrument do?

answers:

What is it?

How much is there?

How does it behave?

How does an instrument work?

Controls the applied probe

measures the systems response

Domain conversion

an analyst seeks to measure the physical or chemical properties of a system, an instrument creates an electrical signal which represents this data

data proceeds through the instrument where different transducers convert the signal from one domain to another

the analysis of an instrument’s behavior proceeds by characterizing it as a sequence of data domain converters which can each be analyzed separately

two types of transducers

input transducer: converts data from a non-electrical domain to an electrical domain

output transducer: converts data from an electrical domain to a non-electrical domain

two types of domains

non-electrical: physical and chemical, scale position, number

electrical: current, voltage, frequency, serial/parallel. analog, time, digital

reference standard

many measurement devices involve a difference detector and a reference standard — the magnitude of the signal generated arises from the difference between the sample under test and the reference standard

signal

every analytical procedure depends upon a signal which is derived frm the output of the detector

some analytical instruments have a non-zero output, even when no target is present. this is called background or baseline

the analytical signal is the difference between the output amplitude and the expected baseline

noise

there are other variations in the output signal level that can occur at all frequencies and constitute an unwanted random or almost random time-dependent changes in the output. these variations are collectively called noise

the noise is measured in the same units as the signal

signal-to-noise

the determination of the magnitude of the signal requires measuring the difference between the background and the sample signal

this measure is blurred by the presence of noise

the ratio of the two dictates the measurability of the signal level

How to evaluate instrumental method performance?

performance characteristics and figures of merit

precision

mutual agreement of measurements, result of random error

accuracy

how close the average value is from the correct one

arises from determinate/non-random errors

“error of the mean”

sensitivity

refers to a techniques ability to detect changes in the signal property

how much does the signal change for a change in the measured variable

slope tells us this — large slope=high sensitivity

calibration sensitivity

S=mC+Sbl

S is signal

m is slope

C is concentration

Sbl is blank signal (y intercept)

detection limit

the smallest amount of analyte that can be reliably detected

analysis signal must be larger than blank signal

quantitation limit

smallest amount of analyte where the concentration can be accurately detected

linearity limit

as concentration/intensity increases, every detector stops responding linearly at some point

identifies the upper limit of concentration to which the technique can be successfully applied

its origin can be electrical or mechanical

linear vs dynamic range

linear range is between LOQ and LOL

where the technique is useful

dynamic range is the range between points at which you can no longer detect any changes in response from the analyte

selectivity

we look for a signal that comes from a specific analyte

but we obtain a signal that may have a contribution from everything that is present in the sample

what determines selectivity?

• differential interactions between analytes and phases, based on things like size, polarity, volatility, temperature, etc

calibration methods

external standard - separate, known standard solutions

internal standard - adds a different, known compound to the sample and standards

standard addition - adds a known amount of the analyte itself to the sample to overcome matrix interference

calibration curve

uses least squares approach to find the trendline

the slope is the calibration sensitivity

internal standard

add a known amount of analyte (standard) similar to the analyte of interest to the sample

measure response of analyte and standard

need to know response factor

can correct for many matrix interferences

response factor (F)

ideally = 1

in a complete circuit…

current has the same value at every point in the circuit

potential is the same from source to load

+ive current leaves device through positive terminal, energy added to circuit

current convention

all matter consists of positively charged nuclei surrounded by an equal number of negatively charged electrons

electrical devices function by controlling the flow of electrons

electrical circuits have always been analyzed on the assumption that electrical current is a flow of positive charge

all circuit behavior is based on this assumption, even though we know electrons are moving

so, electrical current flows from a region of positive potential energy to a region of more negative/less positive potential energy

charge

measuring in coulombs (C) and represented by Q

charge of one electron is 1.6022E-19 C

in one mole of electrons, there is 96,485 C of charge, Faraday’s constant

The Faraday constant is

the charge of one mole of electrons

potential difference or voltage

the potential energy difference between two charged

measured in joules of energy per coulomb of charge, the Volt

1 V = 1 J/C

an electric field exists between two separated charges, where emf changes continuously when moving from one charge to the other

mobile charges

an ion is formed when an electron is removed from or added to a neutral atom or molecule

metals have free electron flow bc valence electrons are shared

other materials share electrons very specifically and are insulators

Mobility

current density has the property of charge that passes through a unit area per second, C/cm^2*s. this depends on the number density of carriers, given as n (particles/cm³), the charge Q of each carrier, and the velocity of the carriers v

J=nQv

the velocity depends on the charge of the particle and strength of the electric field causing it to move. each material is different and presents a different ease of motion for migrating particles, m

v=QEm

the definition is generally done to combine the particle’s charge and ease of motion into a single variable, called the mobility mu

μ = Q m

Conductivity

we can combine expressions for J and v and get charge density

J=EQ²nm… and with z different carrier types, we write J as

J=EQ(n1μ1+n2μ2…)

the term in the summations are constant for a specific type of material under certain conditions. this constant of the material is called the conductivity, sigma

 = Q (n1 μ1 + n2 μ2 + ... + nz μz)

resistivity

the reciprocal of conductivity

J=E/p

Ohm’s Law

V=IR

Power

the rate at which energy is dissipated in the resistor

P=IV

P is in J/s, or Watts

Kirchhoff’s Current Law

at any junction in a circuit, the algebraic sum of the currents is equal to 0

Kirchhoff’s Voltage Law

around any complete loop in a circuit, the algebraic sum of the potential differences is 0

resistors in series

behave as if they were a single resistor whose value was the sum of all individual resistors

resistors in parallel

behave as if they were a single resistor whose resistance value was the reciprocal of the sum of all the reciprocals of the individual resistances

voltmeter

measures voltage, has some internal resistance

loading error

if the source resistance is appreciable in magnitude, to that of the meter’s resistance, a voltage measurement will be in error

the meter resistance must be very large to guard against this error

meter resistance should be several orders of magnitude higher than the source resistance

active circuit elements

add energy to the system

AC or DC power source, batteries, transistors, photodiodes

passive circuit elements

do not produce energy, but could store energy

resistors (dissipate energy in the circuit)

inductors (store energy in a magnetic field)

capacitors (store energy in an electric field)

capacitors

two metallic sheets, separated by an insulator

stores energy in electric field

current relates to changing potential

capacitance (C, farad) is a coefficient relating current and changing potential

inductors

a wire wrapped into a coil, often around a ferrite core

stores energy in magnetic field

potential relates to changing current

inductance (L, henry) is a coefficient relating voltage and changing current

resistors, capacitors, and inductors tend to ______ the current flow in a circuit

impede

resistance (R)

measures a resistor’s ability to impede current flow

reactance (X)

measures a capacitor’s or inductor’s ability to impede current flow

impedance (Z)

the overall impedance in a circuit is the result of the cumulative effect of the circuit’s resistance and reactance

operational amplifiers

an integrated circuit that can amplify weak electric signals

two input pins and one output pins

three critical connections in op amps

inverting input (-)

non-inverting input (+)

output

op amps often used for…

precise measurements of voltage, current, and resistance, which are variables in transducers employed in today’s chemical instruments

basic properties of op amps

high input impedance

large gain (B=10^5-10^6)

Voutput equation

Basic operating principles of op amps

1. it draws negligible current into its inputs

2. an op amp has such a high gain that the voltage difference between its inputs is approximately zero

3. it is an active device, which drives its output from its power supply. its response is limited ultimately by what its power supply can deliver

Which statement is wrong about an
operational amplifier?
A) It can be used to measure current, voltage, or
resistance.
B) Vo=AVin
C) The current through the input impedance is almost
zero.
D) None of the above

D

Comparator

compare two input voltages and output a signal that indicates which voltage is higher

when Vin is on the inverting input, Vo assumes the reverse sign; a non-inverting comparator can be formed by switching the input and reference

closed loop configuration

op amps are employed usefully when the output signal is fed back into one of the inputs through some passive electronic device

voltage follower

an op-amp circuit where the output voltage exactly matches the input voltage (gain of 1) but provides high input impedance and low output impedance

a nearly ideal buffer to protect high-impedance sources from being loaded

so, output voltage = input voltage

V+=Vo

voltmeter

measures voltage — voltage measurements must be interpreted as a voltage divider network

every voltage source has some internal resistance

every voltmeter has some internal resistance

the voltage being measured across the meter’s internal resistor is in proportion to its resistance ratio with the source’s internal resistance

voltage amplifier

most widely used op amp configuration

boosts a weak input voltage signal to a stronger output signal

the output voltage is scaled to the input voltage by the ratio of the two resistors

the gain of the circuit is now controlled by the resistor values and not the inherent op amp open loop gain

if Rf is larger than Rin, we have an amplifier

if Rf is less than Rin, we have an attenuator

current follower

configuration that converts small input current into an output voltage that can be easily measured

integrator

uses an operational amplifier and a capacitor to perform mathematical integration, producing an output voltage proportional to the integral over time of its input voltage

the input current demands a matching feedback current which is delivered by the op amp by changing the output voltage

differentiator

operational amplifier circuit that produces an output voltage proportional to the time derivative (rate of change) of its input voltage

switches the capacitor and resistor in the integrator circuit

Which of these statements is incorrect
A. The Op Amp has inverting and non-inverting inputs
B. The Op Amp is considered as active component of electrical
circuit
C. The Op Amp exceeds external power to provide signal
amplification
D. The Op Amp can be used in a spectrometer to measure
chemical properties.
E. All statements are correct

C

digital storage in humans vs. computer

humans use decimal, base 10 number system

computer uses binary, base 2 number system (on/high/1 and off/low10)

advantages of binary numbers

simple, only two options, 0 or 1

unambiguous and clear signals

digital signals can be transmitted directly to digital computers, which means software can be used to extract the information from signal outputs of chemical instruments

converting binary to decimal

multiply each digit by power of two based on place it is

converting decimal to binary

1. find largest power of two smaller than decimal number

2. , make appropriate binary digit ‘1’, subtract that from decimal number

3. repeat

ADC

analog-to-digital converter

outputs digital data

DAC

digital-to-analog converter

outputs analog data

ADC successive approximation

can use logic circuitry and increasinly refine our approximation

start with most significant bit to see if it is greater than the known voltage. if no, increment the next lower bit. if yes, decrement the MSB and increment the next lower bit

n guesses are required to determine a number in the range from 0-2^n-1

analog vs digital data

Analog data is a continuous signal that represents information through a varying physical measurement, like a record's grooves, while digital data is a discrete signal composed of distinct binary values (zeros and ones) that computers use to represent information

signal

the difference between the sample and the blank response

background or baseline

the residual signal associated with an instrument’s blank response

drift

when the baseline changes slowly with time

noise

random, time-dependent change in the instrument’s output signal that is unrelated to the analyte response

makes the measurement of a sample, blank, and baseline less certain

how to use noise to determine accuracy of a measurement

measure the intensity of the noise and comparing it to the signal

root-mean-square noise

squaring the difference makes everything positive (Navg would be kinda useless)

RMS error is commonly used to calculate noise

basically just the standard deviation formula

sources of electrical noise

thermal, shot, flicker, and interference

thermal noise

aka white noise, arises because the atoms of a solid-state conductor are vibrating at all temperatures and they bump into conductors (electrons), which imposes a new, random motion on those conductors which generates noise

how to reduce thermal noise

cool temperature

reduce bandwidth

shot noise

aka quantum or Schottky noise

arises because charge and energy are quantized

electrons and photos leave sources and arrive at detectors as quanta; while the average flow rate may be constant, at a given instant there are more quanta arriving than at another instant

there is a slight fluctuation because of the quantum nature of matter

how to reduce shot noise

reduce bandwidth. but again, lower noise level comes at the expense of only being able to measure slow enough processes

flicker noise

also known as 1/f noise or pink noise

origins are uncertain. depends upon material, design, nature of contacts, etc

flicker noise is determined for every measurement device. it is recognized by its 1/f dependence

most important at low frequencies

ling term drift in all instruments comes from flicker noise

measurements taken above 1 kHz can neglect flicker noise

modulation

a way to reduce flicker noise — modulates the signal to a higher frequency, amplifies, then demodulates

interference

aka environmental noise or electrical pickup

broadcasts electric and magnetic fields

how to reduce interference

shielding, eliminate ground loops, rigidly fix all cables and detectors, isolate from temperature variations, compensating magnetic fields, etc

software methods

computers can help pull the signal out of the noise

ensemble and boxcar averaging

ensemble averaging

noise is randomly distributed but signal is not. adding two runs together, the signal increases and the noise usually smooths itself out

signal increases with a factor of N but noise increases as a factor of square root N

hence, the S/N ratio increases as a factor of square root N

boxcar averaging

enhances the signal-to-noise of an analytical signal by replacing a group of consecutive data points with its average

Which of these statements is incorrect? (multichoice)

A. noise is only present in the sample response

B. drift only happens to the baseline

C. baseline is basically the blank response

D. the signal equals sample response minus blank response

A,B,C

Which of these statements is incorrect?

A. The thermal noise is lower at lower temperature

B. The flicker noise is higher at higher frequency

C. The shot noise can be reduced by reducing the bandwidth

D. The constant-Y baseline noise is easier to deal with than a noisy instrumental drigt

B