Help with Maxwell-Wien Bridge

Precisely.

No, R = sqrt(3) * X_L.

Reason goes back to geometry:

You have a right triangle between the phasor representing resistor voltage and inductor voltage. The hypotenuse is the total voltage. The total current has the angle of the hypotenuse, because I = V / (R + jwL), the impedance is the vector sum of R and Z_L. (j = sqrt(-1), w = 2*pi*F. Quantities are plotted on the Cartesian plane with real --> x and imaginary ("times j") --> y.)

If you take the angle of the applied voltage as zero, then the hypotenuse of the voltage phasors lies on the real (x) axis, and the opposite corner (the right angle) traces out a semicircle as frequency varies.

The current phasor is parallel with the resistor voltage phasor, because I = V/R has no phase shift.

At high frequencies, normally X_L is very high and almost all the voltage is dropped across the inductor. The picture is a very thin triangle, and Vo ~= Vin because length(long side) ~= length(hypotenuse).

At low frequencies, that short side gets longer (more drop across the resistor, less drop across the inductor), until when they are equal, the power has dropped by half (P --> P/2 means V --> V/sqrt(2)). Of course, an isosceles right triangle has the sqrt(2) proportion and 45 degree angles, so the phase shift is 45 degrees and the output voltage (equals the inductor voltage) is sqrt(2) times less than the supply voltage.

You can find the -6dB point by inspection and basic geometry: it will be a

30-60-90 triangle.

HTH,

Tim

--
Seven Transistor Labs 
Electrical Engineering Consultation 
Website: http://seventransistorlabs.com

You can see much better what is going on if you put this problem in LTspice. When XL = R, both have 0.707 of the applied voltage across them.

The following model omits core loss, permeability changes with frequency and drive level, errors due to stray capacity of the measuring probe, the frequency response of the transformer, and all other losses.

This is at the same time the major strength of SPICE and its greatest weakness. It allows you to isolate the effects to include only the ones you want, but at the same time it can result in models that are far from reality. Only experience can teach you how to include the effects you want to see and how to evaluate the difference between your model and reality.

In this case, modeling a transformer is highly non-trivial, especially in the case of this one. The frequency response is so poor it would probably be impossible to even come close to the actual performance, and certainly not worth the waste in time and effort.

However, the simplified LTspice model can show you how sensitive the setup is to stray capacity. It only takes 27pF to put the inductor into resonance, at which point the voltage across the resistor drops to zero.

Since the distributed capacitance across the winding is far greater than that, there is a serious question of how this measurement is giving valid results.

If nothing else, hopefully this introduction to LTspice may be the most beneficial part of the whole exercise. It has a very steep learning curve, but it allows you to see things you could never find on the bench.

There are two files. Save the first portion to a file with the extension ".ASC", and the second to the same file but with the extension "PLT".

Load the file into LTspice and run. It will plot the voltage across the inductor and resistor as separate waveforms. Then change the parallel capacitance to something other than zero, perhaps 10pF. Note the change in the voltages.

Clearly, there is something wrong with the measurement.

Here is the circuit file:

Version 4 SHEET 1 1204 680 WIRE 416 -64 400 -64 WIRE 512 -64 416 -64 WIRE 704 -64 592 -64 WIRE 736 -64 704 -64 WIRE 816 -64 736 -64 WIRE 400 -48 400 -64 WIRE 816 -48 816 -64 WIRE 704 -32 704 -64 WIRE 400 48 400 32 WIRE 704 48 704 32 WIRE 816 48 816 32 FLAG 400 48 0 FLAG 816 48 0 FLAG 736 -64 Vout FLAG 416 -64 Vin FLAG 704 48 0 SYMBOL voltage 400 -64 R0 WINDOW 3 -39 145 Left 2 WINDOW 39 0 0 Left 2 SYMATTR Value SINE(0 1 1007) SYMATTR Value2 AC 1 SYMATTR InstName V1 SYMBOL res 608 -80 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R1 SYMATTR Value 5650160 SYMBOL ind 800 -64 R0 SYMATTR InstName L1 SYMATTR Value 893Hy SYMBOL cap 688 -32 R0 SYMATTR InstName C1 SYMATTR Value 0pf TEXT 384 -248 Left 2 ;'Inductor Series Voltage Drop TEXT 744 -216 Left 2 !.options plotwinsize=0 TEXT 744 -168 Left 2 !.options nomarch TEXT 744 -192 Left 2 !.options numdgt=15 TEXT 384 -216 Left 2 !.tran 10m TEXT 592 96 Left 2 ;NOTE: Set C1 to 27.97pF for resonance

Here is the PLT file:

[Transient Analysis] { Npanes: 1 { traces: 2 {524290,0,"V(vout)"} {524291,0,"V(vin,Vout)"} X: ('m',0,0,0.001,0.01) Y[0]: ('m',0,-0.8,0.1,0.8) Y[1]: (' ',0,1e+308,20,-1e+308) Volts: ('m',0,0,1,-0.8,0.1,0.8) Log: 0 0 0 GridStyle: 1 PltMag: 1 PltPhi: 1 0 } } [AC Analysis] { Npanes: 1 { traces: 1 {524290,0,"V(vout)"} X: ('M',0,0.001,0,1e+006) Y[0]: (' ',0,3.16227766016838e-005,9,1) Y[1]: (' ',0,-100,20,100) Volts: ('m',0,0,0,-0.8,0.1,0.8) Log: 1 2 0 GridStyle: 1 PltMag: 1 PltPhi: 1 0 } }

** SNIPPED due to aioe **

Rather FINE reasoning. I objected on the basis that nobody makes INDUCTORS like that.

That looks like an interstage audio transformer from a very early tube radio. They were used more for voltage gain than impedance matching, which didn't help the sound quality. Something Atwater Kent would have used.

--
Anyone wanting to run for any political office in the US should have to 
have a DD214, and a honorable discharge.

Catalog lists it as a Plate to grid transformer.

Hey 70Hz to 3000Hz Bell would be proud.

Mikek

And not as fragile.

--
Anyone wanting to run for any political office in the US should have to 
have a DD214, and a honorable discharge.

That IS an interstage transformer.

Maybe.

--
Anyone wanting to run for any political office in the US should have to 
have a DD214, and a honorable discharge.

Now that I think about it, it wasn't Bell, it was Bell Labs that decided 300Hz to 3000Hz is all the bandwidth needed for speech intelligibility. Re: The phone system. I sold the book (Audio Cyclopedia 1969) that I learned that from many years ago for $10, recently I wished I still had it. It had old technology in it back when read in the 70s. I searched a week ago and found it on Amazon for $200 other places up to $637. Ah, just did another search looks like I can get it from Germany for $74. OK, found the mother load on Amazon from $74 to $833. I probably don't want it that bad.

Amazon Reviews,

Mikek

Mikek