IN designing a good sound system, it is necessary to know the true voice-coil impedance with the actual load. The nominal impedance (usually that at 400 or 1,000 cycles) is insufficient. The true impedance at some resonant frequency may be as much as ten times the nominal value stated by the manufacturer. If both the impedance of the voice coil and the input to the speaker transformer can be measured over the entire frequency range, the voice coil can be checked for spurious resonances.
The method described in this Section can also be adapted to measure other impedances, as those of recording cutters and magnetic recorders.
Fig. 701. Equivalent circuit of loudspeaker showing voice-coil components.
Variation of voice-coil impedance with frequency, together with the d.c. resistance, gives a good indication of the efficiency of the speaker. A good speaker (including its baffle or flare) has an almost constant impedance. A cheap speaker has pronounced peaks -the impedance at the bass peak may be many times that at mid-frequencies.
Knowing the correct impedance of a speaker is especially important if the speaker is used in combination with one or more other speakers.
Multiple speaker connection techniques are described in Section 5.
Several speakers in parallel might be used to supply sound to various locations; or several might be used at one location, each covering a different frequency range. In either case correct impedance matching is essential for best results.
What does speaker impedance mean? It is defined as the ratio of the voltage across the speaker voice coil to the current flowing through it (both measured in r.m.s. or both in peak values): E Z = - What makes up impedance?
Fig. 702. Voltmeter-ammeter method of impedance checking.
As shown in Fig. 701, the voice-coil impedance is made up of the ohmic or d.c. resistance of the wire, radiation resistance due to the dissipation of energy in the form of sound, mechanical resistance because the spider and cone rim are not perfectly flexible, and a number of reactances (which change with frequency). The inductive reactances -those which increase with frequency -include that due to the number of turns in the coil and the mass of the diaphragm. The capacitive reactances (inversely proportional to frequency) include those due to the stiffnesses of spider and cone rim.
There is also a reactance due to the elasticity of the air directly in front of the diaphragm.
Methods of measuring Just as there are two main methods for measuring resistance--the Ohm's law method and the Wheatstone bridge -so there are two main methods for measuring impedance! In the Ohm's law method, using the formula Z = E/I, where Z = impedance in ohms, E = potential difference in volts, and I =. current flowing in amperes, all we need to do is pass an alternating current of suitable frequency through the voice coil and make two measurements (see Fig. 702). In fact if we have an a.c. supply of constant voltage, we could calibrate an a.c. ammeter to read the impedance directly in ohms.
Fig. 703. Bridge for measuring high impedance speakers.
Fig. 704. Measuring speaker impedance with a voltmeter, resistor, and
oscillator.
Fig. 705. Typical speaker impedance curves.
Bridge method
For very precise impedance measurement there is nothing superior to an a.c. bridge -balance being necessary for both the resistive and reactive components (Fig. 703). While the bridge method will yield accurate results it is rather tedious, and a faster method is better for the service technician and amplifier designer.
Voltage comparison method
If the same current flows through two components in series, the voltage across those components will be proportional to their impedances. If Z = E/I, then Z is proportional to E if I is constant.
To measure the impedance of a loudspeaker (or other non-resistive load) the oscillator, speaker and a 10-watt resistor are connected as shown in Fig. 704. The resistor should have about twice the rated impedance of the speaker under test. The resistor value should be known accurately. The plan is to measure the voltage across the speaker and to compare it with the voltage across the resistor over the audio-frequency range. Since the resistor and speaker are in series the current through both is the same and the impedance of the speaker can be calculated from the following formula:
Ez Z s = R E R
where Z z is the speaker impedance, R is the resistor in ohms, Ez is the voltage across the speaker, and ER is the voltage across the resistor. The oscillator is first set at 1,000 cycles and the amplifier output is adjusted so that conveniently measureable voltages are obtained across both the resistor and the speaker. It is a good point to have the sum of the two voltages less than the maximum of the meter scale in use so that you will not have to change the scale at any possible impedance.
If you have an insensitive voltmeter you may have to have the volume rather loud in order to get readings, but if the neighbors and amplifier can stand it the results will be just as good. Voltage readings are taken across the standard resistor and across the speaker. It is a good plan to start at 1,000 cycles and to sweep continuously down the audio spectrum to 20 or 30 cycles. Since some speakers may have several closely adjacent peaks, a number of measurements should be made in these ranges to get an accurate picture of the impedance curve. One method is to leave the voltmeter across the speaker after each measurement and to note the significant peaks and valleys as the oscillator is tuned up and down. Readings are made at these peak points along with enough in-between measurements to draw a good curve.
After covering the bass range, the spectrum from 1,000 cycles up should be checked. A smoother curve is usually found in this range, but the technique of continuously sweeping the oscillator up and down the scale will reveal any peaks which exist. The voltage readings are then converted to impedance values.
Fig. 705 presents some typical speaker-impedance curves. Curve A is that of a single-cone 15-inch speaker in an open-back cabinet. Curve B is the same 15-inch speaker in a 7-cubic-foot bass-reflex corner cabinet. Curve C is a two-speaker system with dividing network at 800 cycles. Both speakers are horn-loaded. It is immediately apparent that though all these speakers are rated at 16 ohms, such a rating is only nominal, and much higher impedances are actually present at many frequencies. The high-impedance peaks in the bass range are produced whenever there is a tendency for the voice coil to resonate, either because of resonances in the speaker itself or in combination with the air loading in the cabinet. These peaks in the bass range tell us a good deal about the speaker system. The fairly smooth rise of impedance at the higher frequencies is due to the inductance of the voice coil.
This inductance is really too high in the treble range but is needed in the bass. In dual-voice-coil speakers or two-speaker systems this impedance rise can be eliminated by designing each driver for its particular response range.
The high peak in curve A occurs at the resonant frequency of the speaker cone. Mounting the speaker in an open-back cabinet has done little to damp this resonance and seems to have added a couple of new ones at higher frequencies. In the reflex cabinet the air loading raises the frequency at which the cone resonates but reduces the amount of resonance and adds a lower frequency resonance of the reflex cabinet.
These effects can be seen in the impedance curves which are very helpful in adjusting reflex baffles. The horn-loaded speakers show a more uniform impedance curve down to the bottom peak. This peak is at the cutoff frequency of the horn and the resonant frequency of the low-frequency driver. The driver has been selected to resonate at this point to hold up the low-frequency response where the horn falls off.
It might well be asked, why the speaker impedance rises at these resonant points. It is helpful to look at it this way. The a.c. voltage from the amplifier sends current through the voice coil so that it vibrates in the magnetic field of the speaker. This vibration of the coil in the magnetic field causes it to generate an a.c. voltage of opposite sign to the driving voltage. When a resonant frequency is reached the mass of the voice coil and cone just balances the compliance of the cone and the air chamber, and the coil vibrates back and forth much more vigorously. The voltage generated by the voice coil increases, opposing the driving voltage and reducing the current. Thus the impedance of the unit rises. This is a desirable counterbalance because it is important to reduce the power input at these resonant points to avoid a loudness peak. However, if the amplifier has a high internal impedance, as the speaker impedance rises, the voltage across the speaker will also rise, thus increasing the tendency to resonate, and creating a peak. See Section 8 for methods employed in calculating the internal impedance of an amplifier.
As an example of this condition, Fig. 706 shows the frequency response as measured across the voice coil of a 15-inch speaker in a 7-cubic-foot bass reflex corner baffle when driven by amplifiers of different damping factors. These curves were determined by varying the internal impedance of a high-quality amplifier.
Fig. 706. Effect of amplifier damping factor on speaker response.
In all these cases the amplifier produced a flat frequency curve into a resistor load. The frequency deviations shown are simply the effects of the variations in speaker impedance with the variations in both frequency and the damping factor of the amplifier. Note that with damping factors of 8 or higher the effect on the response of even large changes in speaker impedance is negligible. With a damping factor of 4 the rise in frequency response is just noticeable. With factors of 2 or 1 the bass peaks are pronounced and may be noticeably boomy.
Another important angle is the damping effect of the amplifier on the natural speaker system resonances when the system is subjected to sudden bursts of tone or transient impulses. These shock impulses tend to throw the speaker into vibration at its resonant points unless the speaker is critically damped. Part of this damping is provided in the construction of the speaker itself; part is supplied by the air loading of the cabinet or horn and by the internal impedance of the amplifier. Damping is not greatly affected when the amplifier internal impedance drops to less than 1/8 or 1/10 of the voice coil resistance.
You will be on safe ground if your amplifier has a damping factor of at least 3 over the entire range of audibility.
Internal impedance measurements are therefore important tests for amplifier constructors. When coupled with speaker impedance measurements the information gained can be used to improve the over-all audio performance considerably.
Using an oscilloscope
A more interesting method of determining voice-coil impedance uses an oscilloscope as a voltmeter and has the advantage that both voltages are indicated simultaneously on the screen. As shown in Fig. 707, both the voice coil and a calibrated variable resistor are connected in series and the voltages are applied (via the amplifiers of the scope) to the vertical and horizontal plates.
Fig. 707. How to use an oscilloscope to compare voltages and impedances.
Here is the procedure: First replace the voice coil by a known resistance (say 5 ohms), and adjust the variable resistor to the same value. Now adjust the sensitivity controls of the oscilloscope amplifiers to give a trace consisting of a line at a 45° slope on the screen. This adjustment is important. The horizontal width of the trace must be exactly equal to the vertical height as shown in Fig. 707. After this adjustment, which equalizes the vertical and horizontal scope amplifier sensitivities, the controls must not be moved. The 5-ohm fixed resistor is replaced by the voice coil; and from here on there are two ways to proceed.
Method A: Without touching any oscilloscope control and leaving the variable resistance set at 5 ohms, measure carefully the horizontal width w and the vertical height h of the trace. Both measurements should be in the same units.
Now the impedance is calculated from the formula Z = 5h/w ohms
This method is handy if a large number of measurements are to be made, and should be used if the trace is very different from a straight line. (It will probably be a narrow ellipse.)
Method B: Do not touch the oscilloscope controls. Readjust the variable resistor until the trace is symmetrical about a 45° line (so that the width and height of trace are equal). The voice-coil impedance is then equal to the value of the variable resistor. This method is useful if the trace is very nearly a straight line -the trace will be a straight line at one or more frequencies when the voice coil acts as a pure resist. One of those frequencies is very close to the bass resonant frequency. This method is also better for small oscilloscopes using cathode-ray tubes 2 inches or less in diameter.
Whichever method is used, it is interesting to study the variation in impedance with the type of baffle used. Even if a hand is placed in front of the speaker, a distinct change will occur in the oscilloscope trace as impedance varies.
In all this work a source of audio-frequency voltage is required.
Such an oscillator should have an output of at least 5 volts across a load of 10 ohms for low-impedance work. For high-impedance measurements an output of 20 volts across 10,000 ohms is required. These out puts are low and easily satisfied by commercial oscillators.