Ae104aHomework#4
Development of an indirect counterbalanced pendulum opticallever thrust balance for micro to
millinewtonthrustmeasurement.ByA.N.GrubiiandS.B.Gabriel:
Meas.Sci.Technol.21105101(2010).
AsummarybyGarrettLewisandDustinSummy.
A device is devel

7. Signal and its Conditioning
Suggested reference: Holman
7.1 Digital techniques
Figure 1: Digital coding system: sample and quantise.
Sample and Hold (S&H): samples the input and holds its value constant while the A-D
converts it.
A-D converter: conve

Figure 1: Time histories: sine wave, sine wave plus random noise, narrow bandwidth random
noise, wide bandwidth random noise (B&P, gure 1.11, p.16).
16
Figure 2: Autocorrelations: sine wave, sine wave plus random noise, narrow bandwidth
random noise, wide

3.3 Denitions and Tools
Heaviside (step) function
H (x) =
0
1
2
1
x>0
x=0
x>1
(1)
The step function can be used to write nite integrals as integral over the whole axis:
b
[H (x a) H (x b)] f (x)dx
f (x)dx =
a
Dirac delta function
13
(x) =
0
x=0
x=0
(2)

2.2 Introduction to block diagrams
Block diagram : a shorthand pictorial representation of the relationship between input
signal and output signal. May also include a reference signal.
Element : a system component, which has a transfer function that rel

We must measure what is measurable and make measurable what cannot be
measured. (Galileo, 1610)
Figure 1: The pipe ow experiment of Osborne Reynolds (1883). He described the similarity
of transition of pipe ow from laminar to turbulent (via the Reynolds n

Ae/APh 104a
Experimental Methods
TOPICS TO BE COVERED
1. Introduction to scientific experiments:
1.1 What is a scientific experiment?
1.2 Why do we make measurements?
1.3 The role of theory, generalization and formulation
1.4 The road map for a successful

Ae/APh 104a
Experimental Methods
2010-2011
Description: Lectures on experiment design and implementation. Measurement methods,
transducer fundamentals, instrumentation, optical systems, signal processing,
noise theory, analog and digital electronic fundam

Ae/APh 104a
Experimental Methods
2010-2011
There is plenty of literature available on the topics to be covered in this class. The
main references given here cover key elements of the course and more specific
texts are suggested for additional reading. A c

Ae/APh 104a
Mid-term Solutions, 2010
1/2 [30pts]
(a)[3 pts]
The motion of the diaphragm is opposed by the inertia of the diaphragm,
acoustic damping and an acoustic stiness, such that, per unit area,
P = (mx + x + kx),
with
Q = x.
Then for a harmonic sign

Ae/APh 104a
Homework
Solution Set #5
1/4 Recall the ideal op-amp assumptions: v+ = v in all cases and no current
across the input terminals.
(a) Integrator
v = v+ = 0,
iR =
vin 0
= iC .
RF
So
iC = C1
and
vout =
dvout
dt
1
RF C 1
vin dt
for vout = 0 at t

Ae/APh 104a
Homework
Solution Set #3
1/3
(a) Looking at a free body diagram of the piston, we can see that movement in
the x direction would cause an opposing force from the spring and the damper.
A summation of the forces gives:
mx = k1 x c(x y ) P0 A +

Ae/APh 104a
Homework
Solution Set #2
Issued: October 12, 2010
1/3 Hot wire
(i) (a) To nd the relationship between the mean voltage, Ew , the mean uid
temperature Ta and the mean ow velocity U , substitute for h in equation (2)
to get
2
Ew
Rw
= dw l(Tw Ta

Ae/APh 104a
Homework
Solution Set #1
1/2 Microcalorimeter. (10 points)
For small changes in temperature around an equilibrium given by (Ta , Te , Tl , V ),
where (Ta , Te , Tl ) are the temperatures of the absorber, the electron system and
the lattice sys

Ae/APh 104a
Homework
Problem Set #6
DUE: Friday, December 10, 2010, 5pm to Prof. McKeons oce
Complete at least three of the four exercises below. The exercises require the
use of the Cann Laboratory (see rules for use distributed at the start of term
and

Ae/APh 104a
Homework
Problem Set #5
ISSUED: Thursday, November 11, 2010
DUE: Thursday, November 18, 2010 (in class)
1/4 Basic op-amp circuits
By nding expressions for the output in each case, determine the functions of
the following op-amp circuits:
(a)
(

Ae/APh 104a
Homework
Problem Set #4
ISSUED: Tuesday, November 2, 2010
DUE: Tuesday, November 9, 2010 (in class)
You will be assigned in class an archival paper from the October edition of the
journal Measurement Science and Technology : Meas. Sci. Technol

Ae/APh 104a
Homework
Problem Set #3
ISSUED: Tuesday, October 19, 2010
DUE: Tuesday, October 26, 2010 (in class)
1/3 The device shown below is a proposed design for a pressure transducer in
which the gage pressure P is indicated by the displacement y .
(a)

Ae/APh 104a
Homework
Problem Set #2
ISSUED: Tuesday, October 12, 2010
DUE: Tuesday, October 19, 2010 (in class)
1/3 For a segment of an innitely long wire placed normal to a ow of air
that has mean velocity U and mean temperature Ta , a simple heat transf

Ae/APh 104a
Homework
Problem Set #1
ISSUED: Tuesday, October 5, 2010
DUE: Tuesday, October 12, 2010 (in class)
1/2 A microcalorimeter is designed to measure the power of an incoming photon stream by converting it to a change in temperature in an absorber,

Ae/APh 104a
Mid-term exam, 2010
Issued: Thursday, October, 28th, 8am
Due: Friday, October 29th, 7pm (to 120 Karman)
RULES FOR THE EXAM:
3
1. The exam must be written during one sitting of 2 4 hours (the clock starts
as soon as you start writing). However

Ae/APh 104a
Final exam, 2010
Issued: Wednesday December 8, 8am
Due: Friday December 10, 5pm (to box outside 120 Karman)
RULES FOR THE EXAM:
1. The exam must be written during one sitting of 3 hours (the clock starts
as soon as you start writing). However

Ae/APh 104a
Final exam
Solutions
1/3 [20pts] (a) [2pts] Using the ideal op-amp assumptions, V+ = V = 0 such
that V1 = R1 I1 and Vw = Iw Rw = IF RF , and I1 = IF .
Thus, substituting for IF = I1 = V1 /R1 ,
Vw = V1
RF
.
R1
(b) [6pts] Want to relate Vs to Vw