can we implement a circuit whose amplitude frequency is RC low pass but phase ahead?

[xuexucheng]

My Thread: Laplace transform and fourier transform can not be discussed again, so I start this new thread.

can we implement a circuit whose amplitude frequency is same as the RC low pass filter but phase frequency is ahead not lagged?
do not talk about stable problem.
I want to know can we implement this circuit?
If we can not implement this circuit, why? could you explain in a stratiforward way.

 

[FvM]

Depends on. If you assume a minimum phase system, than the relationship of magnitude response to phase response requires the well known lowpass phase characteristic. If you allow an arbitrary group delay, than you can implement other phase responses as well.

 

[LvW]

My Thread: Laplace transform and fourier transform can not be discussed again, so I start this new thread.

can we implement a circuit whose amplitude frequency is same as the RC low pass filter but phase frequency is ahead not lagged?
do not talk about stable problem.
I want to know can we implement this circuit?
If we can not implement this circuit, why? could you explain in a stratiforward way.

Hello,

the concept of transfer function - including magnitude and phase response - is based on the steady state of a system only.
For this reason, you can discuss the question of phase response not without discussing stability matters.
An unstable system never reaches the steady-state condition - thus, a phase function cannot be measured.
However, theoretically it can be calculated and simulated - however, without relation to reality.
I will give you an example later (because I have to leave now).

 

[LvW]

Hello,

here comes my example: A real opamp model (LM741) with resistive positive feedback (9k--1k).

For the simple assumption that the opamp can be modelled as a single-pole model it is possible
* to calculate the resulting transfer function (without consideration of the bias point problem), and
* to simulate the circuit (bias point and ac simulation).

The results are shown in the attached pdf document.
The circuit has one real and positive pole, however, gain and phase is computed and displayed by the program.

By the way: The program makes no errors. One could measure something like that also in hardware under the condition
that (a) there will be no power switch-on (power available since minus infinity) and (b) absolute constant power and (c) absolute constant element values (also inside the opamp).
These conditions are satisfied during simulation but never can be met in reality.
Counter example: As soon as you perform a tran analysis, the circuit goes into saturation.

Now the question: Does the transfer function that is given in the attachement "exist"? (Such a question was discussed in another thread extensively)
My answer: A function never "exist". Instead, a function is a property (characteristic) of a technical system, which can be measured under certain conditions. If you can establish such conditions - OK. Otherwise it is pure theory that, however makes sometimes sense.
A similar question was discussed also in this forum some time ago: Do negative frequencies exist?
Some people say "yes", some say "no". My opinion: Of course, the don't exist. But they are a nice tool to simplify some mathematical operations.

That's all.
LvW

 

[xuexucheng]

I have understood what you've said.
magnitude and phase response - is based on the steady state of a system only---yes, the textbook told us about this. I think this is the critical to understand.
However, I can not follow your example.
from positive feedback, seems we can not get the 1/(1-jw)
could you explain your example much in detail.
thanks in advance.

Hello,

here comes my example: A real opamp model (LM741) with resistive positive feedback (9k--1k).

For the simple assumption that the opamp can be modelled as a single-pole model it is possible
* to calculate the resulting transfer function (without consideration of the bias point problem), and
* to simulate the circuit (bias point and ac simulation).

The results are shown in the attached pdf document.
The circuit has one real and positive pole, however, gain and phase is computed and displayed by the program.

By the way: The program makes no errors. One could measure something like that also in hardware under the condition
that (a) there will be no power switch-on (power available since minus infinity) and (b) absolute constant power and (c) absolute constant element values (also inside the opamp).
These conditions are satisfied during simulation but never can be met in reality.
Counter example: As soon as you perform a tran analysis, the circuit goes into saturation.

Now the question: Does the transfer function that is given in the attachement "exist"? (Such a question was discussed in another thread extensively)
My answer: A function never "exist". Instead, a function is a property (characteristic) of a technical system, which can be measured under certain conditions. If you can establish such conditions - OK. Otherwise it is pure theory that, however makes sometimes sense.
A similar question was discussed also in this forum some time ago: Do negative frequencies exist?
Some people say "yes", some say "no". My opinion: Of course, the don't exist. But they are a nice tool to simplify some mathematical operations.

That's all.
LvW

 

[LvW]

...........
However, I can not follow your example.
from positive feedback, seems we can not get the 1/(1-jw)
could you explain your example much in detail.
thanks in advance.

Assuming that the circuit can have a bias point within the linear range of the amplifier (or forgetting that, in reality, this cannot happen) you can use the classical formula from H.S. Black to calculate the gain of an amplifier with feedback:

H(s)=Hf*Ao/(1-Hr*Ao) with Hf=R2/(R1+R2)=9/10 and Hr=R1/(R1+R2)=1/10 and Ao=wt/s.

This results in the formula given in the attachement.

I repeat, that - of course - this is a pure theoretical calculation because this function has a pole in the RHP and the circuit will go into saturation immediately after power switch-on. However, the simulator does the same as I did above:
Calculation assuming ideal conditions.
(Comment: It is something like balancing on a razors edge).

Another justification for the impossibility of a rising phase characteristic in real systems:
Think of the group delay that is defined as the negative slope of the phase function. A rising phase would result in a negative delay resp. a negative group velocity over a large frequency range.
Is this possible? Answer: In general not possible!
However, some circuits can exhibit in a very small frequency region a negative group delay - for example in bandstop filters or other filters with a zero (Chebyshev, Cauer/elliptical). But that is a special case.