Electrical characteristics of a dynamic loudspeaker
Encyclopedia
Loudspeaker
A loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...
's driver is its electrical impedance
Electrical impedance
Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...
as a function of frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
. It can be visualized by plotting it as a graph, called the impedance curve.
Explanation
The most common driver type is an electro-mechanical transducerTransducer
A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...
using a voice coil
Voice coil
A voice coil is the coil of wire attached to the apex of a loudspeaker cone. It provides the motive force to the cone by the reaction of a magnetic field to the current passing through it...
rigidly connected to a diaphragm
Diaphragm (acoustics)
In the field of acoustics, a diaphragm is a transducer intended to faithfully inter-convert mechanical motion and sound. It is commonly constructed of a thin membrane or sheet of various materials. The varying air pressure of the sound waves imparts vibrations onto the diaphragm which can then be...
(generally a cone
Speaker cone
A speaker cone, loudspeaker cone or diaphram can be manufactured from various materials depending on driver implementation , desired frequency response for each driver, and cost....
). Other types have similar connections, though differing in detail, between their acoustical environment and their electrical properties.
The voice coil in moving coil drivers is suspended in a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
provided by the loudspeaker
Loudspeaker
A loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...
magnet
Magnet
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, and attracts or repels other magnets.A permanent magnet is an object...
structure. As electric current flows through the voice coil (from an amplifier), the magnetic field created by the coil reacts against the magnet's fixed field and moves the voice coil (and so the cone). Alternating current will move the cone back and forth.
Resonance
The moving system of the loudspeaker (including the cone, cone suspension, spider and the voice coil) has a certain massMass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
and compliance
Stiffness
Stiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body.-Calculations:...
. This is most commonly likened to a simple mass suspended by a spring
Spring (device)
A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...
that has a certain resonant
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
frequency at which the system will vibrate most freely.
This frequency is known as the "free-space resonance" of the speaker and is designated by Fs. At this frequency, since the voice coil is vibrating with the maximum peak-to-peak amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
and velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
, the back-emf generated by coil motion in a magnetic field is also at its maximum. This causes the effective electrical impedance of the speaker to be at its maximum at Fs, shown as Zmax in the graph. For frequencies just below resonance, the impedance rises rapidly as the frequency approaches Fs and is inductive
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
in nature.
At resonance, the impedance is purely resistive
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
and beyond it—as the impedance drops—it behaves capacitively
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
. The impedance reaches a minimum value (Zmin) at some frequency where the behaviour is fairly (but not perfectly) resistive over some range. A speaker's rated or nominal
Real versus nominal value
In economics, nominal value refers to a value expressed in money terms in a given year or series of years. By contrast, real value adjusts nominal value to remove effects of price changes over time...
impedance (Znom) is derived from this Zmin value (see below).
Beyond the Zmin point the impedance is again largely inductive and continues to rise gradually. The frequency Fs and the frequencies above and below it where the impedance is Zmax/√2 are important in determining the loudspeaker's T/S parameters
Thiele/Small
"Thiele/Small" commonly refers to a set of electromechanical parameters that define the specified low frequency performance of a loudspeaker driver. These parameters are published in specification sheets by driver manufacturers so that designers have a guide in selecting off-the-shelf drivers for...
which can be used to design a suitable enclosure for the driver, especially for low frequency drivers. Note that Fs is itself one of the T/S parameters of the loudspeaker.
Load impedance and amplifiers
The variation in loudspeaker impedance is a consideration in audioSound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
amplifier
Electronic amplifier
An electronic amplifier is a device for increasing the power of a signal.It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude...
design. Among other things, amplifiers designed to cope with such variations are more reliable. There are two main factors to consider when matching a speaker to an amplifier.
Minimum impedance
This is the minimum value in the impedance vs. frequency relationship, which can sometimes be slightly higher than the DC resistance of the voice coil, i.e., as measured by an ohmmeterOhmmeter
An ohmmeter is an electrical instrument that measures electrical resistance, the opposition to an electric current. Micro-ohmmeters make low resistance measurements. Megohmmeters measure large values of resistance...
. Minimum impedance is significant because the lower the impedance, the higher the current must be at the same drive voltage. The output devices of an amplifier are rated for a certain maximum current level, and when this is exceeded the device(s) sometimes, more or less promptly, fail.
Nominal impedance
Due to the reactive nature of a speaker's impedance over the audio band frequencies, giving a speaker a single value for 'impedance' rating is in principle impossible, as one may surmise from the impedance vs. frequency curve above. The nominal impedanceNominal impedance
Nominal impedance in electrical engineering and audio engineering refers to the approximate designed impedance of an electrical circuit or device...
of a loudspeaker is a convenient, single number reference that loosely describes the impedance value of the loudspeaker over a majority of the audio band. A speaker's nominal impedance is defined as:
The graph above shows the impedance curve of a single loudspeaker driver in free-air (unmounted in any type of enclosure). A home hi-fi loudspeaker system typically consists of two or more drivers, an electrical crossover network
Audio crossover
Audio crossovers are a class of electronic filter used in audio applications. Most individual loudspeaker drivers are incapable of covering the entire audio spectrum from low frequencies to high frequencies with acceptable relative volume and lack of distortion so most hi-fi speaker systems use a...
to divide the signal by frequency band and route them appropriately to the drivers, and an enclosure that all these components are mounted in. The impedance curve of such a system can be very complex, and the simple formula above does not as easily apply.
The nominal impedance rating of consumer loudspeakers systems can aid in choosing the correct loudspeaker for a given amplifier (or vice versa). If a home hi-fi amplifier specifies 8 ohm or greater loads, care should be taken that loudspeakers with a lower impedance are not used, lest the amplifier be required to produce more current than it was designed to handle. Using a 4 ohm loudspeaker system on an amplifier specifying 8 ohms or greater could lead to amplifier failure.
Impedance Phase Angle
Impedance variations of the load with frequency translate into variation in the phasePhase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
relationship between the amplifier's volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...
age and current outputs. For a resistive load, usually (but not always) the voltage across the amplifier's output devices is maximum when the load current is minimum (and the voltage is minimum across the load) and vice-versa, and as a result the power dissipation in those devices is least. But due to the complex and variable nature of the driver/crossover load and its effect on the phase relationship between the voltage and current, the current will not necessarily be at its minimum when the voltage across the output devices is maximum - this results in increased power dissipation in the amplifier output stage which manifests as heating in the output devices. The phase angle varies most near resonance in moving coil loudspeakers. If this point is not taken into consideration during the amplifier design, the amplifier may overheat causing it to shut down, or cause failure of the output devices. See Power factor
Power factor
The power factor of an AC electric power system is defined as the ratio of the real power flowing to the load over the apparent power in the circuit, and is a dimensionless number between 0 and 1 . Real power is the capacity of the circuit for performing work in a particular time...
for more detail.
Damping issues
Amplifiers present a relatively low impedance to the loudspeaker which acts as a generator when a coil is moving in a magnetic field. This is the so-called back EMF.Characteristically, solid state
Solid state (electronics)
Solid-state electronics are those circuits or devices built entirely from solid materials and in which the electrons, or other charge carriers, are confined entirely within the solid material...
amplifiers have had much lower output impedances than tube amplifiers. So much so that differences in practice between a 16 ohm nominal impedance driver and a 4 ohm nominal impedance driver have not been important enough to adjust for. Damping factor (ratio of output impedance (amplifier) to input impedance (driver voice coil)) are adequate in either case.
Tube amplifiers have sufficiently higher output impedances that they normally included multi-tap output transformer
Transformer
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...
s to better match to the driver impedance. Sixteen ohm drivers (or loudspeakers systems) would be connected to the 16-ohm tap, 8 ohm to the 8 ohm tap, etc.
This is significant since the ratio between the loudspeaker impedance and the amplifier's impedance at a particular frequency provides damping (i.e., energy absorption) for the back EMF generated by a driver. In practice, this is important to prevent ringing or overhang which is, essentially, a free vibration of the moving structures in a driver when it is excited (i.e., driven with a signal) at that frequency. This can be clearly seen in waterfall measurement plots. A properly adjusted damping factor can control this free vibration of the moving structures and improve the sound of the driver.
Further reading
- Designing, Building, and Testing Your Own Speaker System with Projects by David B.Weems (McGraw-Hill/TAB Electronics, ISBN 0-07-069429-X)
- Loudspeakers, Dynamic, Magnetic Structures and Impedance EIA RS-299-A standard