Dette er ikke blot en bas-forstærker..!

En lille konstruktion som flytter resonansfrekvensen (f.res.) og det totale Q (Qtc) for et lukket kabinet ned i frekvens både f.res. og Qtc..

Har du en Bas på 55Hz (f.res.) og Q på 1,2 - flytter dette lille kredsløb det til 19Hz og et Q på 0,5 !


( men se også impuls gengivelsen er blevet meget bedre.. )


På Dansk:














9 - 12 dB/oct highpass equalization ("Linkwitz Transform", Biquad)

A majority of drivers exhibit second order highpass behavior because they consist of mechanical mass-compliance-damping systems. They are described by a pair of zeroes at the s-plane origin and a pair of complex poles with a location defined by Fs and Qt. The circuit above allows to place a pair of complex zeroes (Fz, Qz) on top of the pole pair to exactly compensate their effect. A new pair of poles (Fp, Qp) can then be placed at a lower or a higher frequency to obtain a different, more desirable frequency response.
This allows to extend the response of a closed box woofer to lower frequencies, in the above circuit example from 55 Hz to 19 Hz, provided the driver has adequate volume displacement capability and power handling. The equalizer frequency response is shown below, correcting for a woofer with peaked response (Qp = 1.21) and early roll-off (Fp = 55 Hz), to obtain a response that is 6 dB down at 19 Hz and with Q = 0.5 .

The associated phase and group delay responses are shown below.

Not only is the frequency response extended, but the time response is also improved, as indicated by the reduced overshoot and ringing of the lower cut-off highpass filter step response.

It can be seen from the s-plane description of the transfer functions that the complex poles of the driver in the box are canceled by a set of complex zeros in the equalizer. The specified real axis poles of the equalizer, together with the driver zeros at the s-plane origin, determine the overall loudspeaker response in frequency and time.

The equalizer action is difficult to visualize in the time domain, because the driver output waveform is the convolution of the input signal s(t) with the impulse response of the equalizer h1(t), which in turn must be convolved with the impulse response h2(t) of the driver. Convolution is a process whereby the current value of the time response is determined by the time weighted integral over past behavior. Below are the responses of driver, equalizer and driver-equalizer combination, if the input signal s(t) is an impulse.

More illustrative are the responses to a 4-cycle, rectangular envelope 70 Hz toneburst s(t). For example, the driver output is the convolution of the burst s(t) with the driver's impulse response h2(t). Note that the driver phase leads the input signal, as would be expected for a highpass response. Upon turn-off of the input burst at 57.14 ms the driver response rings towards zero, governed by Fp = 55 Hz and Qp = 1.21.

The equalizer output response lags its burst input. This signal will force upon the driver a response correction so that it is no longer dominated by Fp = 55 Hz and Qp = 1.21. The equalizer output signal is convolved with the impulse response h2(t) of the driver to obtain the desired equalized driver output. Now, the decay of the driver output follows the 2nd order highpass filter response determined by Qp = 0.5 and Fp = 19 Hz of the equalizer, after the excitation has stopped.
Of course, none of the driver mechanical parameters like mass, compliance and damping have been changed in the process of equalization, only the input signal to the driver has been modified.

The above circuit can also be used to correct the low frequency roll-off of a tweeter so that the equalized tweeter becomes a filter section in an exact LR4 acoustic highpass. (f0Q0fpQp.gif, pz-eql.xls, f0Q0.gif, FAQ15, sb80-3wy.htm, sb186-48.gif , sb186-50.gif)