Dear Biswajit,

welcome,

It seems that your op amp is saturated and no longer working as an amplifier.  Such integrator circuits without  DC gain limiting will tend to saturate and the output voltage of the amplifier gets clamped to either DC power supply values. Consequently, there is no sense to speak from miller effect. It is apparent from your results that the input impedance of the amplifier will be a low resistance. This is a consequence of op amp saturation. You can check the mode pf operation by determining the DC operating condition of the amplifier you will find that the output voltage is approaching one of the rail values of the DC power supply.

Best wishes

Biswajit,

Are you "looking into the inverting input node"

by using SPICE simulator ?  

Glen Ellis sir,

Yes ,your assumption is right.

Most likely because the models are quite limited: you may expect the modelling of "side-effects" of 1st order, but rarely something beyond that. And for OpAmps I'm certainly not the only one considering the Miller C as not being a side-effect of 1st order.

Dear Biswajit

Would you please show the circuit and specify more your question?

best wishes

Think about derivation in the appendix :-)

Biswajit,

By using SPICE simulator you are probably using Linear Equations 

for devices modeled with certain limitations.  

(1) Linear Equations do not properly / exactly show

the real Non-Linear World.

(2) Your Spice model must include the Miller characteristics

else your Spice algorithm will not calculate for Miller characteristics.

Examine your models for Spice

... everything is some kind of aproximation.

I repeat Dr. Zekry's request for the Spice Program and your schematic.

Dear Biswajit,

The derivation of  Josef shows that the input impedance of the miller integrator at the inverting input of the amp depends on the frequency as according to the Miler theorem the  Miller capacitance will be seen at the input multiplied by (1+A) where A is the absolute value of the voltage gain of the amplifier . One has to add also the the input impedance of the real op amp which will appear in parallel with the effective input miller input capacitance. Then if you speak about an input impedance which is independent of frequency, then there will be some assumptions or approximations that led to this result.  Therefore, i would urge you to display your circuit together with magnitude of the impedance at the inverting input.

Best wishes

As far as I understand , there is no escape from Miller's capacitance even in an opamp .They are parasitic and inherent by virtue of reactance  of the circuit level & frequency.

Now , what happens is the capacitance blends with lumped parameters say when you do capacitive coupling or the aggregate in input or output impedance .

If we use an opamp with a cascode at the input, the "internal Miller phenomenon" is negligible.

The integrator with 100k as Ri and 1nF as Cf has a break at about 8 milliHz (equivalent of time constant of  20sec)  and is equivalent of a low pass filter with a dc gain of 106 dB and RC of 100k*200uF.  The huge capacitance of 200uF is the effect of miller effect. the results are from simulation using circuit maker.... using 741 Note that the positive input should be grounded through a 100k as well else, the amplifier will be in saturation  and affects the simulation.

 It is well known that the capacitor multiplier is expected to be Av or about 200,000 times giving miller capacitance of 200000 Cf (= 200uF with Cf as 1nF)for 741.  You may use a simulation tool and make your observations. Do not forget that the voltage at -ve input is amplified by 200000 and appears at output.  The input impedance is very much frequency dependent.

One can also use LF353 with open loop reduced to 100,000 and confirm the results.. In this case the capacitance is effectively 100k*100uF= 10 sec time constant 

Feedback requested.

Dear Abdelhalim Zekry sir

Please find the attachment of circuit diagram below.

Biswajit,

 You need to reduce the current source value to 1pa, and also intruduce a 79 nA current source flowing into the op amp on the positive side to keep proper dc conditions at op amp output. Otherwise, simulator results are not believable, it looks [ as confirmed by simulation with circuit maker].And then see the frequency response [dB versus log f] from 1 MilliHz onwards to say 1kHz. or 100hz

FB requested

The behavior of the op amp depends on resistances connected at its input (of source). The current source has infinite resistance and dc conditions have to be proper before you simulate to find ac response. Please note. May I know what simulator you are using. If it is free I can try with THAT simulator!

Dear Biswajit,

welcome,

It seems that your op amp is saturated and no longer working as an amplifier.  Such integrator circuits without  DC gain limiting will tend to saturate and the output voltage of the amplifier gets clamped to either DC power supply values. Consequently, there is no sense to speak from miller effect. It is apparent from your results that the input impedance of the amplifier will be a low resistance. This is a consequence of op amp saturation. You can check the mode pf operation by determining the DC operating condition of the amplifier you will find that the output voltage is approaching one of the rail values of the DC power supply.

Best wishes

I agree with Abdelhalim Zekry, this circuit connection does not give an best amplifier and consequently the Miller theorem will not work.

I agree with respectable colleagues.

However, may I know about the type of current source you used? is it IAC or IDC ?

Also, which simulation profile do you used to draw Bode plot? AC sweep ?

Thanks.

Rohith

The answer is simple: The opamp-based MILLER integrator block works only as desired because of the MILLER effect. This was clearly explained by V.s.V Mani in his answer. This effect enlarges the feedback capacitor by a factor equal to the open loop gain of the amplifier. Thus, we have a very large time constant equivalent to a very small pole frequency of the resulting lowpass function (which may be used as an integrator)