charlie@oakhill.UUCP (Charlie Thompson) (09/07/89)
I have a question for the netland filter jocks out there... For years I have seen a 3 op-amp filter structure known as a 'state variable' or 'biquad' filter. The filter provides simultaneous highpass, lowpass, and bandpass outputs. I understand how the filter works but WHY is it called a 'state variable' / 'biquad' filter??? State variables come from linear system theory ... why does this filter attract the name? can't any filter have state variables?? Biquadratic relates to the fact that the filter has 2 integrators making it 2nd order...o.k. lots of filter structures can be 2nd order and they don't even need 2 op-amps to be 2nd order! So why the name biquad? Trivially yours, Charlie -- WB4HVD
myers@hpfcdj.HP.COM (Bob Myers) (09/08/89)
>For years I have seen a 3 op-amp filter structure known as a >'state variable' or 'biquad' filter. The filter provides simultaneous >highpass, lowpass, and bandpass outputs. I understand how the filter >works but WHY is it called a 'state variable' / 'biquad' filter??? >Biquadratic relates to the fact that the filter has 2 integrators >making it 2nd order...o.k. lots of filter structures can be 2nd order >and they don't even need 2 op-amps to be 2nd order! So why the name >biquad? No, a circuit can be "2nd order" without being "biquadratic", or even, for that matter, having two integrators. It's the order of the polynomials in the transfer function that counts (basically, the number of poles/zeroes), which pretty much translates into the number of reactive components (outside of things like bypass caps and the like). Two integrators certainly can make a second-order system, but it's not the only one possible. Actually, the name "biquadratic" comes from the fact that the design realizes a biquadratic transfer function; i.e., one of the form 2 F(s) = K (s + (z1+z2)s + z1z2) ------------------------ 2 s + (p1+p2)s + p1p2 where z1, z2, p1, and p2 are the zeroes and poles, respectively. The "state-variable biquad" is one name for this three-amplifier realization of a biquadratic transfer function, but I'm not certain how "state variable" got hung on this particular circuit. (There is at least one other three-amp biquad circuit to which I have found reference: the "feedforward three-amp biquad".) Bob Myers KC0EW HP Graphics Tech. Div.| Opinions expressed here are not Ft. Collins, Colorado | those of my employer or any other myers%hpfcla@hplabs.hp.com | sentient life-form on this planet.
markf@amc-gw.UUCP (Mark Freeman) (09/09/89)
In article <17660018@hpfcdj.HP.COM>, myers@hpfcdj.HP.COM (Bob Myers) writes: > >works but WHY is it called a 'state variable' / 'biquad' filter??? > > a biquadratic transfer function, but I'm not certain how "state variable" > got hung on this particular circuit. (There is at least one other three-amp I believe the term "State Variable" is applied to this circuit, because the terms of the State Coefficient Matrix apply directly to the amplifier transfer functions. Thus, you can go back and forth between the matrix representation and the circuit readily. Take this explanation with a grain of salt, as it comes from someone who has worked on software and digital hardware for the last 10 years. -- Mark S. Freeman Applied Microsystems Corp. markf@amc.com amc-gw!markf
johns@eecg.toronto.edu (David Johns) (09/09/89)
In article <17660018@hpfcdj.HP.COM> myers@hpfcdj.HP.COM (Bob Myers) writes: >>For years I have seen a 3 op-amp filter structure known as a >>'state variable' or 'biquad' filter. The filter provides simultaneous >>highpass, lowpass, and bandpass outputs. I understand how the filter >>works but WHY is it called a 'state variable' / 'biquad' filter??? > (Part about biquad deleted) >The "state-variable biquad" is one name for this three-amplifier realization of >a biquadratic transfer function, but I'm not certain how "state variable" >got hung on this particular circuit. (There is at least one other three-amp >biquad circuit to which I have found reference: the "feedforward three-amp >biquad".) > > >Bob Myers KC0EW HP Graphics Tech. Div.| Opinions expressed here are not > Ft. Collins, Colorado | those of my employer or any other >myers%hpfcla@hplabs.hp.com | sentient life-form on this planet. I believe that the term "state-variable" is used since this particular configuration realizes the "direct-form" implementation of a state-variable filter. In other words, at the output of the two integrators one has 1/e(s) and s/e(s), where e(s) is the pole polynomial. Since the numerators of these two integrator output are quite simple, it is an easy matter to sum them together and create an arbitrary zero polynomial and therefore an arbitrary biquadratic function. (To create a filter with a non-zero gain at infinity, one has to also sum up the input signal.) It is interesting that this direct-form (direct-form is used in the control literature) filter structure is quite poor for higher order filters but is almost optimum for the second order case. (For active filter designers, the high order case of the direct-form structure is often called companion-form filters.) David Johns