MAS 836 Sensor Systems for Interactive Environments
Recitation #2 Feb 18th 2010
Nan-Wei Gong
nanwei@mit.edu
Today we will talk a little bit more about the black box…
• Capacitor (Inductor)
-RC circuit
THE Black box!!!
-Time constant
• Complex numbers
-complex plane…
• Decibels (dB)
-cut off frequency
-half power point
-F3dB
• Filters
-Low-pass, high-pass
-MFB band-pass filter
Capacitors
A capacitor or condenser is a passive electronic component consisting of a
pair of conductors separated by a dielectric (insulator such as air)
Parallel plate Capacitor
C, defined as the ratio of charge ±Q on
each conductor to the voltage V between
I, electric current, can be represented as
the time rate of change of charge
dielectric with permittivity ε : farads per meter (F/m)
Electrolytic capacitor
-polarized
It uses an ionic conducting liquid
as one of its plates with a larger
capacitance per unit volume than
other types.
they must be connected the correct way!!
http://en.wikipedia.org/wiki/Capacitor
Unpolarized (fixed)
capacitor
-non-polarized
Small value capacitors are unpolarised
and may be connected either way round.
They have high voltage ratings of at least
50V, usually 250V or so.
Capacitors
This stage could theoretically
Last forever!! But in real life,
We got leakage current from
the insulator
Practical electronics for inventors 2nd edition, Scherz
Capacitors
RC Charging Circuit
1
Vs = RI +
C
Vc = V (1 − e
Time constant
∫ Idt
−t
RC
Fully charged
)
τ = RC
http://www.electronics-tutorials.ws/rc/rc_1.html
Capacitors
RC Discharging Circuit
Fully discharged
1
Vc =
C
∫ Idt
Vc = Vse
Time constant
−t
RC
τ = RC
http://www.electronics-tutorials.ws/rc/rc_1.html
Time varying circuits make things so much more complicated…
You can try to solve the equation with your
super duper partial differential equation solving skills
or…..
Practical electronics for inventors 2nd edition, Scherz
Remember Z in the bucket?
Or… use Z !!!!
C
R
L
Z
Last week, we learned that some guy
decided to put all the crazy math
into a bucket and call it “Z”, the impedance …
now, it’s time for you to use this wonderful bucket
Figures are mostly from Practical electronics for inventors 2nd edition, Scherz
Complex numbers
Practical electronics for inventors 2nd edition, Scherz
R LC in complex form
Practical electronics for inventors 2nd edition, Scherz
Some examples…
Zs in serial, Zs in parallel, Zs in serial and parallel…..
Practical electronics for inventors 2nd edition, Scherz
Input and output impedances
Input impedance Zin tells you how much
current can be drawn into the input of a device.
Output impedance Zout refers to the impedance
looking back into the output of a device
10x rule:
The input impedance of a device should be 10x
Greater than the output impedance of the circuit
supplying the input signal!
10x rule:
The output impedance of a device should be 1/10x
smaller than the load’s input impedance
10x
Quick example about Zin and Zout calculation ..see low-pass filters
Input and output impedances
When input f =0
C is open circuit
Vout = Vin
When input f = infinite
C is short
Vout = 0
Low-pass Filter (RC filter)
Input impedance
Output impedance
Practical electronics for inventors 2nd edition, Scherz
Decibel (dB) and why do we care about it
Decibel (dB) is defined as the power (P) ratio between two signals.
It is used to express the magnitude of a physical quantity
(usually power or intensity) relative to a specified or implied reference level
In the world of electronics, dB is used to define
- Cut off frequency
- f3dB point
- half power point
-…
When the power of a signal is cut in half
dB = 10 log(0.5) = -3dB
Low-pass Filter (RC filter)
Transfer function
Input impedance
output impedance
half power point :
1/2 =
Practical electronics for inventors 2nd edition, Scherz
1
1+ τ ω
2
2
τ = RC = ω −1
Decibel (dB) cont.
Cutoff frequency , f3dB point :
http://en.wikipedia.org/wiki/Low-pass_filter
http://www.atis.org/glossary/definition.aspx?id=3848
Basic Filters
http://www.radio-electronics.com/info/rf-technology-design/rf-filters/rf-filter-basics-tutorial.php#top
Basic Filters
http://www.radio-electronics.com/info/rf-technology-design/rf-filters/rf-filter-basics-tutorial.php#top
Band-pass filter and Q
(normalized…)
First order, second order, third order …..
first order
second order
we can expect a filter of order N to cause the value of
to fall as
Wait!!!!! This is getting too complicated…there’s no way I am going to deal with any N>2…
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/part3/page2.html
http://analogfilter.blogspot.com/2008/06/filter-construction.html
Help me computer!
You can do the simulation in Matlab or several online filter design tools
(Analog Device Interactive Design Tools : OPAMPs: A ctive Filter Synthesis tool)
http://www.isip.piconepress.com/projects/speech/software/demonstrations/applets/util/filter_design/current
/
Use design references (TI references- OPAMPs for everyone)
http://focus.ti.com/lit/an/slod006b/slod006b.pdf
Useful references
How to bias an OPAMP
http://www.media.mit.edu/resenv/classes/MAS836/bias.pdf
OPAMPs for everyone
http://focus.ti.com/lit/an/slod006b/slod006b.pdf
http://library.books24x7.com.libproxy.mit.edu/toc.asp?site=bbbga&bookid=32208