NORTH READING ENGINEERING
NORTH READING, MASSACHUSETTS 01864 USA
  
MODELING THE KLIPSCHORN FOLDED BASS HORN
Part II
INTRODUCTION
With the electrical equivalent circuit model of the Klipschorn developed in Part I it's now possible to explore how various crossover network designs alter the bass horn response.  To recap, the electrical equivalent circuit model for the Klipschorn derived in Part I for both the round and square magnet K33 drivers is shown below.  When executed in a SPICE engine (in this case LTSPICE) each circuit will simulate the impedance presented to the voltage source outputs.  When expressed in terms of dB relative to the input signal of the voltage source (i.e. a 0dB reference), the voltage drop across the throat impedance, Ret, represents the sound pressure level of the bass horn.  For an AC voltage source that sweeps a signal between two frequencies, say 50 to 1000Hz, the frequency dependent sound pressure level of the horn is predicted. 

FACTORY CROSSOVERS
The simulated electrically equivalent responses of the factory Type A, AA, AK, AK2, AK3 and AK4 crossovers is considered. The simulation process consists first of deriving the bass horn response with no crossover (no net).  Here, the voltage level that produces a 0dB reference at the peak horn output is determined by iteration.  All simulations are then performed at that voltage level.  Thus, as different crossover networks are examined changes to the horn response can be assessed as +/-dB changes relative to the response of the horn without a crossover filter, i.e. the "raw" horn response. 

Inductor DC resistances are estimated based on typical values measured for 16AWG, Fe-core types.  The square magnet, K33E woofer is used in the simulations.  As is shown below, the bass filter section from each factory network is executed in the LTSPICE engine by insertion of its components between the voltage source driving the filter and voice coil.  For example, the Type A and AA filter circuit shows a 2.5mH inductor in series between the positive terminal of the voltage source, V3 and the DC resistance of the voice coil, Re (filter components of each factory type are enclosed in the red box).  An AC voltage source with source resistance of 1mOhm and DC offset of 20mV is used as an amplifier model.  The output of each source is set at 5VAC and the frequency is swept between 50-1000Hz.  The current factory production filter, AK5, is not modeled.  The filter schematics can be viewed (and downloaded) by visiting the Klipsch Forum.

FREQUENCY RESPONSE
By comparing the simulation results with the "no net" horn response, the design intent of each network can be proposed.  When compared to the no net response, the simple first order networks A and AA provide about 6dB of attenuation at the 400Hz crossover frequency used in the system.  Above that frequency, the effective attenuation (horn and network) is about 50dB/oct. 

The AK and AK2 nets provide output consistent with the A and AA over the pass-band of the filter but enhance attenuation above the pass-band which, based on the simulation, is about 90dB/oct. 

The AK3 appears to be a minor revision that increases 400Hz output by 3dB with an attenuation above 400Hz consistent with the AK and AK2 nets. 

The AK4 is a significant departure from earlier designs and provides pass-band frequency contouring via notch-filtering over the range of frequencies where the horn sensitivity demonstrates a maximum, i.e. between 100-300Hz.  The result is a somewhat smoother acoustic response with concomitant reduction in sensitivity.  The attenuation above 400Hz is the same as the AK3.

Plot below is same simulation as above but showing responses between 50 and 500Hz.  400Hz crossover frequency to the midrange horn is highlighted.

IMPEDANCE MAGNITUDE
The magnitude of the complex impedance of the horn-network combinations is simulated and plotted below.  A 4Ohm minimum impedance magnitude is seen in all networks expect the AK4 where the effect of the notch filter lowers the minimum to near 2.6Ohm.  For some amplifiers this might prove difficult to drive thus prompting the factory to revise the design to the current production AK5 filter (not modeled). 

The voice coil resistance, Re, is 3.5Ohms.  As is evidenced below, the minimum impedance magnitude is higher and attributed to horn loading which increases the resistance seen by the voltage source. The resistance increase is associated with the radiation resistance of the horn, Ret, reflected back to the voltage source terminals thru the K33E motor assembly.  Note however that the addition of complex conjugate element (i.e. notch filter) can alter, quite significantly, the impedance magnitude measured in the system.    

PHASE RESPONSE
The phase angle over the range of frequencies modeled is shown below for the horn-network combinations considered in this analysis. 

Webpage content property of John Warren of North Reading Engineering, North Reading, MA 01864 USA.  No part of the above work may be copied and published, in part or in total, without written permission.  © 2018 John Warren