Multimeter for Remote Sensing of Resistance
Two Wire Resistance Measurement--Rlead Voltage V lt measuring i circuit of DMM I=IO I=IO Rlead RU
IO
I=IO
Rmeasured = (Vmeasured / I) = ( RU + 2Rlead) Error in measurement is 2Rlead.
4-Wire Remote Sensing
Source Voltage g measuring g circuit of DMM S Sense Sense IO Source I=IO Rlead Rlead I=IO Rlead l d I=IO Rlead
I 0 I=0 I=0
RU
No current flows through g the sense leads. Rmeasured = RU = Vmeasured / IO This more accurate method is recommended for measuring resistance below 100 .
Environmental Specifications
The environmental concerns for DMMs are 1 Temperature 1. 2. Humidity 3. Altitude 4 Sh 4. Shock k 5. Vibration.
Safety Ratings
New DMMs must conform to an IEC 1010-1 standard. (I t (International ti l Electrotechnical El t t h i l Commission) C i i )
Steps in Selecting a DMM
Analyze the Device Under Test
What variables are to be tested?
Analyze the Test Environment
What are the hardware and software interface issues?
What is the range of signal values?
What are the accuracy, resolution and sensitivity requirements? What special DUT characteristics should be considered?
What are the noise problems?
What are the throughput requirements?
What many DUTs are to be tested?
What features necessary?
special are
How effective solution?
cost is the
ATTENUATORS
An Attenuator is a network designed g to introduce a known amount of loss when functioning between two impedances: Z1 = Zsource and Z2 = Zload
Attenuator Z1 Z2
ATTENUATORS
50 50 Load
Source
Attenuator
50
50
General Arrangement of impedance matching of attenuator with source and load
Types:
Analog --- continuously varying Digital/stepped Di i l/ d --- varying i in i steps Balanced/ unbalanced Symmetrical/unsymmetrical Active or/and passive components/devices can be used to construct attenuators
Applications:
In test instruments --- CRO, Multimeters, Signal generators and analyzers g y between source and amplifier & amplifier and load
Basics of Attenuators
A two t port t network t k is i said id to t be b symmetrical t i l if the th input and output ports can be interchanged without altering the port voltages and currents. currents For symmetrical network network Z1 = Z2
Basics of Attenuators
Networks may be either balanced or unbalanced (with respect to ground), depending impedance b t between one input i t and d one output t t terminal t i l should h ld be b equal to impedance between other two terminals.
Basics of Attenuators
Image Impedance:
The input impedance is Z1 when out put is connected to Z2. The out put impedance is Z2 when input is connected t Z1. to Then the impedances Z1 and Z2 are known as the image impedances of the two port network.
Basics of Attenuators
Image Impedance:
The image g impedances p Zi1 = Z1 and Zi2 = Z2 can be written in term of open circuit and short circuit impedances.
z i1 = z io z is
z i 2 = z oo z os
The two port network can not defined by Zi1 and Zi2 so a third thi d parameter t image i attenuation tt ti constant t t is i also l used. z z
k=
is
z io
os
z oo
Basics of Attenuators
Characteristic Impedance:
For symmetrical y network, , the image g impedance p is referred as the characteristic impedance or iterative impedance Zo
z i1 = z i 2 = z o
z o = z io i z is i z o = z oo z os
zo
Attenuator
zo
Basics of Attenuators
Attenuation is measured as a ratio of the incident signal and the signal passing through the output.
Attenuation, = Vin/Vout Attenuation in dB = 20 log (Vin/Vout) Attenuation,
Vin Attenuator Vout
Simplest Attenuator
Potential Divider (L-type attenuator)
R1 Vin R2 Vout
in dB = 20 log (1+R1/R2)
No impedance matching
Symmetrical T Attenuator
R1 R2 R1
Design T attenuator for attenuation and characteristic impedance Zo
Design T attenuator for attenuation and characteristic impedance Zo
R1 R1 R2 Ro
Symmetrical T Attenuator
Ro
Let R2 = mR1 then
R o = R 1 1 + 2m
Then attenuation will be given by R1 R2 Vin i R1 RoVout
1 + m + 1 + 2m = m
Symmetrical T Attenuator
An T attenuator can be designed for given Ro and by y the following g equations. q
1 R1 = Ro 1+ 2 Ro R2 = 2 1
R1 R2 R1
Symmetrical T Attenuator
Example Design a 20 dB dB, 50 T attenuator. attenuator
Solution Here = 10 and Ro = 50 From the equations, we get R1 = 40.9 40 9 & R2 = 10.1 10 1
Cascading T Attenuators:
For high attenuation cascaded network is better then single attenuator network because R2 reduces as increases
2 R2 = 2 Ro 1
R2 may become impracticably small so cascaded network is used to increase overall attenuation. The networks can be cascaded so the over all attenuation increased.
409 101 409 409 101
409 409 409 409
101
Cascading g T Attenuators
Example: Design a 60 dB 500 ohms attenuator.
60 dB 500 ohms attenuator using 3 sections of 20 dB T section attenuators
Cascading g T Attenuators
Example: Design a 60 dB 500 ohms attenuator. 60 dB 500 ohms attenuator using 3 sections of 20 dB T section attenuators
409 409 409
409 409 409 409
101
101
101
Symmetrical Attenuator
R1
R2
R2
Let R2 = mR1. Then
R o = R1 m 1 + 2m
If we connect t a load l d of f value l Ro to t this thi attenuator, tt t then th attenuation tt ti will be given by 1 + m + 1 + 2m = m
Symmetrical Attenuator
Alternately, an attenuator can be designed for given Ro and by the following equations. 2 1 R1 = Ro 2
+1 R2 = Ro 1
Cascading of section networks can be done to achieve higher attenuation levels.
The Bridged T Attenuator
R3
R1 R2
R1
It is assumed that Ro= R1 , and R12 = R2 . R3
= (R1 / R2) + 1 Design Equations R1 = Ro, R2 = Ro / ( - 1), R3 = ( - 1) Ro
Note that R1 is independent of .
Stepped Attenuator
Input
RD RC RB RA
4 2
3
Output O tp t
Stepped attenuator
Multi-range Stepped Attenuator
1 2 3 4 R1 R1 R2 Input 1 4 2 3 1 34 2 1 2 3 4 R3 R3 R4 Output All the switches are ganged
Variable Attenuator
Variable attenuation levels keeping Ro constant. By varying resistors in T or section attenuators, we can get continuously varying attenuators. But all the three resistors need to change simultaneously simultaneously. This may not be an easy proposition. In I bridged b id d T attenuator, tt t R1 is i independent i d d t of f attenuation, R2 decreases and R3 increases with attenuation. Therefore, R1 can be fixed equal to the value of characteristic resistance. Resistors R2 and R3 can be ganged together to vary them simultaneously
Variable Attenuator
R3 R1 R2 R1
Variable attenuation levels keeping Ro constant. R1 = Ro, R2 = Ro / ( - 1), R3 = ( - 1) Ro
Ex.:
Find Fi d out t th the attenuation tt ti and d image i resistances of given attenuator network. 10K
Vin
20K
Vout
Solution:
Ri1 = RinsRino = 17.32K 17 32K Ri2 = RoutsRouto = 11.55K in dB = 20 log (1+R1/R2) = 3.52
Padding
It is possible to design an attenuator, to be i inserted t d between b t source and d load, l d to t provide id proper matching with the load. Such a use of attenuator is called as padding a source. source In many applications, I li ti th source resistance the it may not match with the load. Attenuators will see different resistances at the input and output. output
How the Symmetrical network work for matching?
RS Source R1 mR1 Rout R1
Rout = R1 + mR1 (R1 + RS) U i T attenuator Using tt t equations, ti Ro = R1 (1+2m)
= [(1 + m + 1+2m ) / m] We get,
R
Rout =
+ 1
K 2 / 1
where K = RS / Ro
Variation of Rout with RS Rout =
+
1
Let RS = 0 i.e. K = 0. Then Rout =
2 + 1 1 2 R
0
For RS = i.e. K = , we get Rout =
+ 2
2 1 1 0 R
Larger is the value of i.e. larger is the attenuation, more closer is Rout to Ro.
K 2
K / 1
Variation of Rout with RS
Rout =
+
1
Let Ro = 50 and = 10. F RS = 0, For 0 Rout = 49 ohms. h For RS = , Rout = 51 ohms. Therefore Th f f any value for l of f RS, Rout lies li between b 49 and d 51 ohms. If is increased further, difference between Rout and Ro will reduce.
0 R
K 2
K / 1
E Example l A signal source with an unknown resistance is to be interfaced with a 600 ohms system using a 12 dB 600 ohms pad. Find out the output resistance for the extreme values of source resistance. Solution Att Attenuator t resistance it and d attenuation tt ti = 4 and Ro = 600 ohms. Rout for Rs between zero and infinite, is 528 and 678 ohms.
R di A Reading Assignment i t
2.2 : Digital-To-Analog Converter 2.3 2 3 : Analog Analog-To-Digital To Digital Converter
