This is not usually a major source of error, since the network impedance of a high frequency filter should be low. There is also a small frequency-dependent term to the input impedance, since the effective impedance is the real input impedance multiplied by the loop gain. This means that we probably want to use FET amplifiers with high impedance circuits. This is required so that the input of the op amp does not load the network around it. We assume in the “perfect” model that the input impedance is infinite.
![what is filter keys what is filter keys](https://consumer-tkbdownload.huawei.com/ctkbfm/servlet/download/downloadServlet/H4sIAAAAAAAAAD2Py07DMBBF_8XrgmZsx56wquPEKhvEoqwrp3GCpTat8mgFiH_HqSKWR3M0994fNo9h2H9dA3thyDasudz7FUXCNp7Cmz8vGPqneTzEs-_CAZAyBaA5Pl_7bvXe_fSZvIzLhoLCVsqjzLgmWQueURuobWVT82TX8fu1SerObB9fARSRoCydjkPwU7z0-7iEooJcCpCAALBhY-x6P83DUseSVViCE2CswLJQToHj2hrn8tJBhdwiFUZqVLy0pArSVWGcNbrMEahKWTd_is3H__5pmMOj27p_Z9jvHzoJ-JIgAQAA.png)
In addition to the frequency-dependent limitations of the op amp, other of its parameters may be important to the filter designer. It is also a good idea to have low bias current devices for the op amps so, all other things being equal, FET input op amps should be used. This is easily accomplished using dual op amps. This implies that the loop gain be a minimum of 20 dB at the resonant frequency.Īlso it is generally considered to be advantageous to have the two op amps in each leg matched. To make the circuit work, we assume that the op amps will be able to force the input terminals to be the same voltage. In the FDNR realization, the requirements for the op amps are not as clear. The filter gain must also be factored into this equation. The same rule of thumb as used for the integrator also applies to the multiple feedback topology (loop gain should be at least 20 dB).
![what is filter keys what is filter keys](https://helpdeskgeek.com/wp-content/pictures/2021/09/image-190.png)
As the loop gain falls, the Q of the circuit increases, and the parameters of the filter change. Q enhancement is a problem in this topology as well. The multiple feedback configuration also places heavy constraints on the active element. Because of this, the integrator no longer behaves like an integrator. In other words, the op amp is no longer behaving as an op amp. Without sufficient loop gain, the op amp virtual ground is no longer at ground. The mechanism for Q enhancement is similar to that of slew rate limitation. What happens is that the effective Q of the circuit increases as loop gain decreases. Therefore, an op amp with 10 MHz unity gain bandwidth is the minimum required to make a 1 MHz integrator. What this means is that there must be 20 dB loop gain, minimum. This should be taken as the absolute minimum requirement.
![what is filter keys what is filter keys](https://www.thewindowsclub.com/wp-content/uploads/2019/03/Filter-Keys-Options-Windows-10-600x355.png)
A good rule of thumb is that the open-loop gain of the amplifier must be greater than 10 times the closed-loop gain (including peaking from the Q of the circuit). As an integrator, however, more is required. As amplifiers, the constraint on frequency response is basically the same as for the Sallen-Key, which is flat out to the minimum attenuation frequency. The state-variable configuration uses the op amps in two modes, as amplifiers and as integrators. This causes the filter to lose attenuation. There is also an issue with the output impedance of the amplifier rising with frequency as the open loop gain rolls off. This is because the output of the amplifier is phase-shifted, which results in incomplete nulling when fed back to the input. Beyond cutoff, the attenuation of the filter is reduced by the roll-off of the gain of the op amp. This is because the amplifier is used as a gain block. All that is required is for the amplifier response to be flat to just past the frequency where the attenuation of the filter is below the minimum attenuation required.
![what is filter keys what is filter keys](https://www.howtogeek.com/wp-content/uploads/2009/05/image30.png)
The Sallen-Key configuration, for instance, is the least dependent on the frequency response of the amplifier. How much the frequency-dependent nature of the op amp affects the filter is dependent on which topology is used as well as the ratio of the filter frequency to the amplifier bandwidth. So in simplistic terms, the transfer function of the amplifier is added to the transfer function of the filter to give a composite function. This roll-off is equivalent to that of a single-pole filter. To accomplish this, a real pole is usually introduced in the amplifier so the gain rolls off to <1 by the time the phase shift reaches 180° (plus some phase margin, hopefully). Negative feedback theory tells us that the response of an amplifier must be first order (−6 dB per octave) when the gain falls to unity in order to be stable. This is due mainly to the physical limitations of the devices with which the amplifier is constructed. The most important limitation of the amplifier has to do with its gain variation with frequency. While amplifiers have improved a great deal over the years, this model has not yet been realized. In developing the various topologies (Multiple Feedback, Sallen-Key, State-Variable, and so forth), the active element was always modeled as a “perfect” operational amplifier. The active element of the filter will also have a pronounced effect on the response.