Midrange's crossover analysis

Take this circuit..

Schematic_MFC.png


Some would call this first order with a notch filter.. however it can be used to create a steep slope if you choose the right values. Here is one time I modelled the effect of an existing crossover (link below). The measured response is in red and the model to fit it is blue.

The model is a good fit for response over a span of 40dB, which is more than we'd typically consider important, yet the phase is 2 or 3 orders behind.

https://www.diyaudio.com/community/threads/the-elsinore-project-thread.97043/post-6872695
 
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Take this circuit..

View attachment 1334253

Some would call this first order with a notch filter.. however it can be used to create a steep slope if you choose the right values.
I've modelled the above circuit, and some results are presented below. If the LC leg of the circuit is disabled, we have a first-order filter with a −3dB cutoff frequency of about 4.2kHz. The circuit creates a very steep slope below about 1.8kHz due to the severe notch in the magnitude response, with a great deal of extra phase shift also added to the response.

1721174462135.png


The circuit components used in the above simulation with the LC leg active are shown below.

1721174554936.png


However, if we re-purpose capacitor C2 and place it as follows,

1721174851296.png


we get the following 3rd-order response function, with approximately the same cutoff frequency and quite similar phase response behaviour in the transition band of the filter, between 1kHz and 4.2kHz. The resulting response has much less interaction with the low-frequency response below about 700Hz. The classical 3rd-order filter also appears to have benefits by greatly reducing driver displacement below 1kHz in an ongoing continuous manner, which would be helpful for a tweeter.

1721174986131.png
 
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