Yes I am at a university.But this question was asked to me by a professor in an interview board.I told the same answer as yours.But he was not satisfied with that.So I thought of posting it in the Researchgate hoping to get some interesting replies as the one you have posted above.

Phase shifts can not be introduced to signals by using resistors only. Phase shifts usually require imaginary components that can only be realized by using inductors or capacitors. Even if resistors used in active circuits, still the need for inductors or capacitors to generate the required phase shifts at the desired frequency bands. However, at higher microwave frequencies, normal resistors may manifest some sort of phase shifting effects, and hence micro strip technology, among other techniques, is commonly adopted to fabricate pure resistors, inductors, or capacitors at such high frequencies.  

He asked me to give an example of a passive circuit using only resistors by which you can give a 90 degree phase shift to a signal.

The question is incorrect or incomplete!

A center freq must be specified!

Actually, the resistance is defined following a DC analysis!

In reality, until getting to relativistic physics,  in the Maxwellian physics, some energy boundaries appear existent for a real known (geometry and materials) device through electrical or variable magnetically energy gradient exists This device is not a capacitor or a resistor or an inductor but the equations do point out a phase lag (or a temporary delay). By further modifying the geometry or the materials' properties this effect can be tunned. But the freq. are usually high (at least MHz).

In semiconductors, mixed passive (transmission - line like) and active behavior is a common trait. So, I'd never leave the ground of good electrically conductive metals if I'd be intending an almost ideal resistive behavior. Furthermore, the real geometry is the cause for parasitic reactive effects.

Please note: in electricity the resistance is analyzed in DC mode as there is almost an aberration to do such an analysis in AC and there to remain only a resistive effect.

No.

Hi Renoh,

There is no Phase Shift between the Voltage and the Current in a Resistive(only) Circuit.

However if you professor have something in his mind for switching microstrip lines with different length this is another story :)

Does hi specify frequency? or question was in general is it possible to implement phase shift wit resistive components only

We know that all our definitions are valid under certain restrictions.

Explanations and clarifying question from Mr. Danail Baylov (AD) about the frequency or frequency range seems to me absolutely correct.

suppose simple voltage divider by two resistors, supplied in the upper end with real signal (0' sine wave) and in the bottom end with imaginary signal (90' shifted sine wave). At the middle point between the two resistors you will achieve any phase shift between 0 and 90', depending on the resistor ratio!

cheers :)

I have two ways;

1) create primitive capacitors using PCB patterns.

2) tap a long wire at the 1/4 wavelength point. Build it from wire resistors and you win.

this is not a resistor. this is called 'transmission line' which has lumped RC, LC or RLC equivalent scheme!

Actualy Mr. Dobrev's idea works but it needs either two signals or a signal and a phase shifter. Again, a center frequency must be specified!

@Peter - not possible by summing 0' and 180' !

summing the signal with its 180' copy can change only the amplitude, because 180' shifted signal has no imaginary part. It is an inverted real signal.

phase shift is arctg(Im/Re).

when Im=0, then arctg(0)=0'.

when Re=0, then arctg(infinity)=90'

90' can be achieved by summing equal parts of 45' and 135' shifted signals!

You should read basic books about complex mathematics!

Just to specify that the "simple voltage divider by two resistors supplied in the upper and bottom end with two voltages" is a voltage summer with weighted inputs. The input coefficients are α and 1-α, and they crossfade when changing the ratio between resistances...

Really tricky answer in a de Bono lateral thinking manner... but it is not so correct... since here the resistors do not introduce the phase shift... it is initially introduced by some other device... and the resistors only mix the signals...

With single stimulus - no.

With two stimuli at angle, a perfect constellation would be quadrature, you may continually shift phase to your heart's desire. Using a linear stereo potentiometer with this constellation you may continually shift phase over 180° with only a little amplitude change.

The question does not put any restriction on linearity. Using nonlinear resistors we can, "in principle", achieve a phase shift as follows. However, it is an extremely difficult proposition to synthesize a passive resistive network that will simulate the required function and therefore nobody will do it.

Whenever an ordinary linear time-invariant resistor is concerned, and a single sine wave is given, the answer to the original question is no. No question about it.

In a wider sense, however, a resistor is any two-terminal whose characteristics are fully described in the voltage-current plane (i.e.not involving time derivatives and/or integrals of the terminal voltage and/or of the terminal current). By considering (very unusual) nonlinear resistors and just considering a fixed amplitude sine wave input, you might obtain a phase shift using only nonlinear resistors.

Assume the input signal is vin=Vpk sin(omega*t). Assume that, for a nonlinear resistor, i=i_0*arcsin(v/Vpk) and for another nonlinear resistor v=Vpk*sin(i/i0). If you apply vin across the first resistor, you get a current i_0 (omega*t)mod 2pi flowing through it. Adding a constant offset phi * i0 to that current and then injecting it into the second resistor you will get a voltage vout=Vpk sin (omega*t +phi) across the second resistor. Provided that the above nonlinear resistors are available, you could actually implement the circuit using the first as the input resistor and the second as the feedback resistor in an opamp-based inverting amplifier topology...

Yes, I think so. Specific rime-varying, as well as nonlinear resistor networks behave as phase shifters under very special hypotheses. Actually it is worth noting that their characteristic depends on the characteristics of the input (ampitude, offset, maybe initial phase and frequency for time-varying resistors), so they cannot regarded as the equivalent of a delay-based shifter including memory elements.

Another idea is to use a memristor... that is a kind of (time-dependent) resistor...

@Paolo

flim-flam!

can you make a mathematical  example with e.g. ideal diode as a nonlinear resistor: Id=Is*exp(Vd.q/k/T)

... and one more idea - to use a negative resistor introducing a phase shift of 180 deg between the current and voltage...

not possible, the negative resistor can introduce only the real gain, and the 180' is G=-1.

The answer is hidden in the speed of light, and the resistor is  needed only for a load.

Take  10m cable e.g. copper  wire. Supply it in one end with signal with e.g. 7.5MHz frequency. At the other end, according the speed of light  you will have 33ns delay (td=10/300000000s).

Now, connect one resistor as a load  in the cable free end to ground, and two resistors between the cable ends. Depending on the two resistors ratio you will achieve any phase shift between 0' and 90'. Of course the same can be done simply by trimming the cable length and using the resistor only as a load to ground.

cheers :)

The 180-deg shift is still a phase shift, isn't it? The question does not specify if the shift should be variable... or different from 180 deg...

in real life negative resistor can not be found.

it can be designed by an amplifier and positive resistors but the operation has limited conditions etc.

one additional note:

the cable should be loaded by resistor much lower than the impedance of the free space (

Maybe a differential negative resistor (tunnel diode, Gunn diode, etc.) will do the job?

the tunnel diode should be properly  biased, i.e. it consume energy  and is an active circuitry, a kind of amplifier.

The Russian scientists were rely that tunnel diode will amplify GHz signal from satellite by simple biasing of tunnel diode in its small signal negative rd, but the reliability and repeatability of such "amplifier" was close to zero.

Yes... but we have implicitly accepted that circuits contain sources:)

No. It is not possible. Note that the addition of an inverted signal, weighted by a coefficient, to the original one, will work only if the signal is a pure sinusoid. It is true that, in practice, every signal can be decomposed in multiple sinusoids but, in order to maintain the signal shape going through a delay, the delay of the single sinusoid must be proportional to its  frequency, and this can not be achieved by simple addition (see the definition of group delay). By definition to have a delay you must have a memory, either analog or digital, and resistors, by definition, have no memory.

Yes. It is Possible. You can use a centre tap transformer for 180 degree phase shift.

No. Not possible as the transfer function of a resistor does not include s.