DAMPING, DAMPING FACTOR AND ACTIVE DAMPING CONTROL

Speaker as second order system

A speaker can be viewed as a system with : ď ŹA mass m ď ŹA stiffness k This is a typical 2nd order system with a damping component and a certain resonating frequency.

Modelling the Loudspeaker as a Lumped System (I)

Modelling the Loudspeaker as a Lumped System (I)

Modelling the Loudspeaker as a Lumped System (II)

Modelling a speaker to be driven by an amplifer, an equivalent electric circuit is used. equivalent electrical circuit, Re is the output stage resistance of the amplifer and the connection cables. Le is the reactive part of the voice coil inductance. Revc is the real part of the voice coil inductance. equivalent mechanical circuit, Mm the moving mass. Cm compliance (the inverse of the stiffness) Rm suspension system. equivalent acoustical circuit, Ma models the air mass Ra models the radiation impedance

Speaker Damping

Try to drive a speaker by hand (or with the apposite signal), and the cone will vibrate at a greater amplitude at frequencies close to its natural resonance.  The frequency-response curve of the speaker under these conditions will show a peaked output near cone resonance, usually between 30 and 100 Hz. This kind of oscillation is a form of distortion, and in severe cases it can translate into “one note bass” and not well defned low end. Another effect is the reduced SPL due to the Back Electromotive Force. The amplifer will “see” this Back-EMF and will need to handle it. REMEMBER: Large excursion and heavy diaphragm leads to a higher Back-EMF. The effect of the Back-EMF on the amplifer circuit can be dominant compared to low output impedance (amplifer + cables).

The damping factor

An engineering method to describe the ability of an amplifer to control undesirable movement of the speaker cone Only the resistive parts of source, cable and coil are taken. The source impedance (that is seen by the loudspeaker) includes the connecting cable impedance. A high damping factor is the equivalent of a strong "brake" on the voice coil motion. A high damping factor indicates that an amplifer will have greater control over the movement of the speaker cone,

Cables effect

But what about the cables? Two effects: Dissipative Poor Damping The partitive effect can be compensated with the good old design rule of 5% But how to compensate the damping? Usually a DF > 20 is recommended. Better > 50.

American Wire Gauge 18 → 1.62 mm2 16 → 2.58 mm2 10 → 10.4 mm2

Active Damping control

But how to control the damping factor? Simple! Introduce a negative resistance! Example: R*K=-2 ohm I = 0, Vd=0 V I = 2,Vd=2 V

Ok, not so simple... What if: Z load = 2 ohm? Latency influence on the Phase margin?

Active Damping control

But how to control the damping factor? Simple! Introduce a compensation with a negative resistance!

Z s =Z out +Z cable +Z compensation Z compensation =â&#x2C6;&#x2019;Z cable

Active Damping control

Ok, not so simple... we need a feedback loop and the voltage generator current controlled.

•Example: R*K=-2 ohm I = 0, Vd=0 V I = 2,Vd=2 V

What if: Z load = 2 ohm? Latency influence on the Phase margin?

Active control, possible use

Cable loss compensation Voice coil increase in resistance due to heating compensation, even dynamically adjusted with the estimated voice coil temperature Damping factor “creative” adjustment, to create a more dry and damped or boomy bass response (ie DSP4) Active loudspeakers with reduced loading volume: a negative resistance has the effect of reducing the Qes of the driver, allowing for smaller enclosures for the same driver

Introducing negative feedback in the control loop may bring to accidental yet interesting effects.

Damping factor v1 1
Damping factor v1 1

Cippa lippa!!!