Below is a functional diagram of the bridge. The three configurations for measuring C, L and R are shown.
[attachment=5279]
Consider the operation of the bridge when it is measuring capacitance. Depending on the position of the Q / tanδ switch, the phase balance controls will comprise either a series-connected capacitor and resistor or a parallel-connected capacitor and resistor: the diagram is drawn with the Q / tanδ switch shown in the Q position. In this position, the capacitor and resistor are in parallel. In effect, this means that the bridge is measuring the unknown capacitor with its loss resistance represented as a shunt resistance.
An analysis of operation.
Just by way of a simple illustration of how that all works in practice, let's consider the case of a perfect capacitor (infinite shunt loss resistance) connected at the unknown terminals. For ease of analysis, I will refer to the RANGE variable resistance as R1, the BALANCE variable resistance as R2, the PHASE BALANCE variable resistance as R3 and its parallel capacitor as C1. The unknown capacitor has a reactance of Xc.
Suppose the Q / tanδ switch is in the Q position.
At balance, the standard formula tells us that:
Xc.R2 = R1 (R3||C1), where "||" means 'in parallel with'.
Now introduce our friend, the j-Operator:
-j.Xc.R2 = -j.R3.Xc1 / (R3 - j.Xc1)
It can be shown that that reduces to:
j.Xc(R2.R3 / R1) + Xc.Xc1 = j.R3.Xc1
If we equate the real and imaginary parts, we get:
Xc.Xc1 = 0. That can only be valid if Xc. Xc1 → infinity, so we can ignore that.
We also get:
Xc.[R2.R3 / R1] = R3. Xc1,
from which: Xc = (R1 / R2).Xc1.
Since Xc = 1/wC, nominally, then:
1/wC = (R1 / R2).(1 / wC1),
so: wC = (R2 / R1).wC1,
so: C = (R2 / R1).C1
Now (R2 / R1) is determined by the value of the RANGE (switched) resistance and the setting of the (variable) BALANCE control. Since C1 is known (internally selected), then the value of C, the unknown capacitor, is known.
Note that the actual value of the frequency of the bridge does not feature in that final equation.
When the Q / tanδ switch is in the δ position, the resistor and capacitor in the PHASE BALANCE arm are in series; the resistor will have a different value in this case, say R4.
As before, at balance, we have:
-j.Xc.R2 = R1(R4 - j.Xc1)
And similar results arise . . . .
First, we get: -R1.R4 = 0 . . . . which is clearly an impossibility, and
secondly, we get: Xc.R2 = R1.Xc1,
from which: Xc = (R1 / R2).Xc1 . . . . same result as before.
Of course, we considered a perfect capacitor. If all that analysis is done again, but with the unknown capacitor now replaced by a capacitor and a series loss resistance, say (Rc - j.Xc), a similar, but not identical, pair of results are arrived at.
The same process of analysis is valid for the case of inductance measurement.
For the resistance measurement case, things are a lot simpler: no reactances to consider, so no j-Operator! In actual point of fact, in this case, the bridge simply reduces to nothing more sophisticated than that of the elementary Wheatstone bridge, with the exception that its output is chopped to approx. 100 Hz for application to the amplifier-detector (which uses its own internal a.g.c. loop).
All of that is a huge simplification of the excellent circuit description provided in the Marconi manual. The quality of the build of this item, its ruggedness, the accuracy and precision of its internal standards (R, L and C), the added bits of sophistication in the circuitry and the manual itself all lead me to believe that this piece of test gear must have cost a great deal of money in its day. They don't make test gear like this anymore.
All said.
Al.
[attachment=5279]
Consider the operation of the bridge when it is measuring capacitance. Depending on the position of the Q / tanδ switch, the phase balance controls will comprise either a series-connected capacitor and resistor or a parallel-connected capacitor and resistor: the diagram is drawn with the Q / tanδ switch shown in the Q position. In this position, the capacitor and resistor are in parallel. In effect, this means that the bridge is measuring the unknown capacitor with its loss resistance represented as a shunt resistance.
An analysis of operation.
Just by way of a simple illustration of how that all works in practice, let's consider the case of a perfect capacitor (infinite shunt loss resistance) connected at the unknown terminals. For ease of analysis, I will refer to the RANGE variable resistance as R1, the BALANCE variable resistance as R2, the PHASE BALANCE variable resistance as R3 and its parallel capacitor as C1. The unknown capacitor has a reactance of Xc.
Suppose the Q / tanδ switch is in the Q position.
At balance, the standard formula tells us that:
Xc.R2 = R1 (R3||C1), where "||" means 'in parallel with'.
Now introduce our friend, the j-Operator:
-j.Xc.R2 = -j.R3.Xc1 / (R3 - j.Xc1)
It can be shown that that reduces to:
j.Xc(R2.R3 / R1) + Xc.Xc1 = j.R3.Xc1
If we equate the real and imaginary parts, we get:
Xc.Xc1 = 0. That can only be valid if Xc. Xc1 → infinity, so we can ignore that.
We also get:
Xc.[R2.R3 / R1] = R3. Xc1,
from which: Xc = (R1 / R2).Xc1.
Since Xc = 1/wC, nominally, then:
1/wC = (R1 / R2).(1 / wC1),
so: wC = (R2 / R1).wC1,
so: C = (R2 / R1).C1
Now (R2 / R1) is determined by the value of the RANGE (switched) resistance and the setting of the (variable) BALANCE control. Since C1 is known (internally selected), then the value of C, the unknown capacitor, is known.
Note that the actual value of the frequency of the bridge does not feature in that final equation.
When the Q / tanδ switch is in the δ position, the resistor and capacitor in the PHASE BALANCE arm are in series; the resistor will have a different value in this case, say R4.
As before, at balance, we have:
-j.Xc.R2 = R1(R4 - j.Xc1)
And similar results arise . . . .
First, we get: -R1.R4 = 0 . . . . which is clearly an impossibility, and
secondly, we get: Xc.R2 = R1.Xc1,
from which: Xc = (R1 / R2).Xc1 . . . . same result as before.
Of course, we considered a perfect capacitor. If all that analysis is done again, but with the unknown capacitor now replaced by a capacitor and a series loss resistance, say (Rc - j.Xc), a similar, but not identical, pair of results are arrived at.
The same process of analysis is valid for the case of inductance measurement.
For the resistance measurement case, things are a lot simpler: no reactances to consider, so no j-Operator! In actual point of fact, in this case, the bridge simply reduces to nothing more sophisticated than that of the elementary Wheatstone bridge, with the exception that its output is chopped to approx. 100 Hz for application to the amplifier-detector (which uses its own internal a.g.c. loop).
All of that is a huge simplification of the excellent circuit description provided in the Marconi manual. The quality of the build of this item, its ruggedness, the accuracy and precision of its internal standards (R, L and C), the added bits of sophistication in the circuitry and the manual itself all lead me to believe that this piece of test gear must have cost a great deal of money in its day. They don't make test gear like this anymore.
All said.
Al.
