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by HERMAN BURSTEIN
To get flat, wide-range response from tapes requires equalization, which is frequency alteration in recording and playback to overcome the tape system's inherent frequency deviations. The choice of equalization characteristics interrelates with problems of noise and distortion, and varies among tape types and even among tapes of the same type.
A tape playback head is a "velocity" device, whose out put increases as the signal frequency increases. That is, for a given signal level on the tape, the output of the head doubles if frequency doubles, goes up tenfold if frequency increases by a factor of 10, and so on.
It is more convenient to express this relationship in decibels. For a constant signal level presented to the playback head, as frequency rises output rises just about 6 dB/ octave, or exactly 20 dB/decade. This is true for an "ideal" head, one without losses or other aberrations, as distinguished from actual heads. Today's high-quality heads come quite close to the ideal, but there are still differences of some consequence in the extreme bass and, particularly, in the extreme treble.
Momentarily, let's assume we have both an ideal, lossless tape system which produces a flat recorded signal on the tape and an ideal playback head. Unequalized record-playback response is then the same as the output of an ideal head, shown by curve ABC in Fig. 1. To achieve flat response, it is merely necessary to employ playback equalization which mirrors head output. This is curve DBE, declining 6 dB/octave as frequency rises. (A simple R-C [resistance-capacitance] circuit could readily take care of the matter.) Curve FBG is the resulting flat response.
Figure 1 is not entirely fanciful. At a high tape speed such as 30 ips, the unequalized record-playback response and the required equalization would be very close to curves ABC and DBE. And life would be simple.
But as tape speed is reduced, significant losses appear, particularly in recording. By the time we get down to 1 7/8 ips, these losses are profound. Figure 2 takes us from the ideal world into the real world, showing the typical un equalized record-playback response of a high-quality, two-head cassette deck-in this case, a Harman/Kardon CD391-when using Type II (chromium dioxide or ferri-cobalt) tape. (I am indebted to Peter Philips of Harman/ Kardon for supplying measured data on the CD391's equalization and frequency response, which I used to pro duce Fig. 2 and several other figures.) In Fig. 2 we principally note the huge treble loss, amounting to about 1 dB at 1 kHz and reaching about 41 dB by the time we get out to 20 kHz. This loss is the difference between the ideal, 6-dB/ octave rising response (curve ABC in Fig. 1) and the actual treble response shown in Fig. 2. About 36 dB of the loss at 20 kHz occurs in recording, and about 5 dB in playback.
Treble loss in recording is due mainly to demagnetization. The recorded signal consists, in effect, of a series of bar magnets; as frequency rises they grow shorter (more cycles per second entail more-and necessarily shorter magnets in a 1-S span of tape), so that their opposite poles get closer together and tend increasingly to cancel each other. The erasing effect of bias current is also substantial; this effect increases as frequency rises because high frequencies are not as deeply em bedded in the tape as others. In addition, slight treble loss occurs in the record head due to winding capacitance, eddy currents, and hysteresis.
In playback, treble loss is due mainly to the width of the playback head's gap. The wider the gap, the greater the loss. As frequency increases and the recorded bar magnets grow shorter, gap width approaches magnet width and the resolving power of the gap begins to fail. The record-playback head in a two-head deck ordinarily has a wider gap, and incurs greater treble loss in playback, than the separate playback head in a three-head deck.
Slight additional treble losses occur in the head due to winding capacitance, eddy currents, and hysteresis.
There is some further playback aberration below 40 Hz, too. First, there are several bumps in response, on the order of 0.5 to 1.5 dB. Second, there is a slight up-tilt with respect to the ideal 6 dB/octave response, as shown by the smoothed version of the deck's response. The up-tilt reaches about 3 dB at 20 Hz and makes a slight contribution to the bass boost needed in play back. The foregoing phenomena are due to the "contour effect," whereby the entire head, not merely its gap, reacts to the magnetic flux on the tape.
With the exception of the slight head losses due to winding capacitance, eddy currents and hysteresis, all the losses described above become increasingly severe as tape speed is reduced. It takes just as many flux changes ("bar magnets") to record a given frequency at a slow tape speed as at a high one. But as speed is reduced, the amount of tape that passes the head per second is also reduced, and the magnets must become shorter in order to fit into the allotted length of tape. As we have already noted, the major record and playback losses in crease as the recorded magnets be come shorter. In technical terms, these major losses increase as the recorded wavelength decreases, with wave length in inches being tape speed in ips divided by frequency in Hz.
How Equalization Is Achieved
Figure 2 makes it obvious that, in general terms, bass boost and treble boost are needed to restore flat response. Not obvious is the amount of boost required and whether each kind of boost should be provided in recording or playback. Fortunately we have industry standards, which in broad terms call for the following:
Bass boost is to occur largely in playback; if applied in recording, the vast amount of bass boost needed would overload the tape.
Treble boost is to occur largely in recording. Substantial treble boost in playback would heavily accentuate noise, because great amplification is required for the tiny signal produced by the playback head.
Record-head losses are to be compensated for in recording, play back-head losses in playback.
A specific playback equalization curve is to be followed, depending on tape speed and tape type. This is fundamentally a bass-boost curve, modified (in accordance with the above principle) to compensate for each individual deck's playback-head losses.
Stated differently, the combination of playback amplifier equalization plus head losses must conform to the standard playback curve.
The record equalization is to be such that, in conjunction with standard playback equalization, flat response is achieved. This is largely a treble boost, some of which (usually very little) is to compensate for record-head losses.
We now turn to specifics for cassette-deck equalization. Two standard playback equalization curves are provided for cassettes, as shown in Fig. 3. Curve ABC shows standard playback equalization for Type II (chromium dioxide or ferri-cobalt), Type III (ferrichrome-now little used), and Type IV (metal) tapes.
Curve DBE shows standard playback equalization for Type I (ferric oxide) tapes. It is customary to show these curves using 400 Hz as the reference frequency.
The standards express these curves in terms of turnover (also called transition) frequencies, or in terms of time constants. The relationship between turnover frequency and time constant is f equals 159,155 divided by t, where f is turnover frequency in Hz and t is a time constant given in microseconds.
Correspondingly, t equals 159,155 divided by f.
Curve ABC has designated time constants of 70 and 3,180 uS. Accordingly, the turnover frequencies are 2,274 and 50 Hz. This signifies that bass boost commences at 2,274 Hz (where it is up 3 dB) and levels off at 50 Hz (where it is 3 dB below maxi mum). Curve DBE has time constants of 120 and 3,180 uS, or turnover frequencies of 1,326 Hz and 50 Hz. Total bass boost-from above 20 kHz to be low 20 Hz-is 33.1 dB for the 70-uS curve and 28.5 dB for the 120-uS curve.
Depending on tape type used, a cassette deck is supposed to conform to one of the two playback curves in Fig. 3. It bears repeating that the deck's total response-the combination of its playback-amplifier equalization and playback-head losses, not its equalization alone-must conform to these curves.
To see how this works in practice, let's return to the Harman/Kardon CD391 unit, whose unequalized response is shown in Fig. 2. The equalization supplied by that deck's record and playback amplifiers, and the resulting record-playback response, appear in Fig. 4. Curve ABC, consisting chiefly of bass boost, is provided by the playback amplifier, and curve DBE, consisting chiefly of treble boost, is supplied by the record amplifier. When the equalizations of ABC and DBE are applied to the unequalized record-playback response of Fig. 2, they produce the record-playback response of FBG in Fig. 4, which is substantially flat through the audio range.
It is to be noted in Fig. 4 that segment DB of record curve DBE includes a mild bass boost. This partly compensates for the fact that segment AB of playback curve ABC does not extend linearly all the way to the lowest frequencies but starts to level off (3 dB below maximum) at about 50 Hz-consistent with standard equalization. Further boost at the low bass end is sup plied by the playback head's slight up-tilt, as observed in Fig. 2. The net result of AB in playback, DB in recording, and playback up-tilt is to maintain bass response a little short of flat. As shown by FB, bass response drops slightly below 35 Hz; it is about 1.5 dB down at 20 Hz.
At the extreme high end, we may note in Fig. 4 that this deck's record-playback response exhibits a trivial rise of about 1 dB. This is either be cause of slightly excessive treble boost due to component tolerances in the record equalization, or because the tape to which the record equalization was applied is a bit "hot" at the high end.
How close does actual playback-amplifier equalization (curve ABC in Fig. 4) come to the standard equalization (curve ABC in Fig. 3)? Figure 5 compares the two. In Fig. 5, DBE is the actual equalization and ABC is the standard. The two curves are very close. Below 400 Hz, segment DB of the actual curve is no more than 1 dB away from segment AB of the standard curve. This minuscule difference is probably due to component tolerances. Above 400 Hz, it appears at first sight that the actual and standard segments BE and BC part company too much. But it must be remembered that the industry standard requires the actual curve to include compensation for losses of the playback head. There fore BE includes treble boost, reaching about 5 dB at 20 kHz, which essentially accounts for the difference between BE and BC. If one adds playback-head losses to BE, this brings the curve down so that it becomes BC.
Standardizing Playback Curves
As we shall bring out later, for a given cassette type, it is feasible to use more than one kind of playback curve in terms of the amount of bass boost provided. So why has the amount of bass boost been standardized? And why are there two standard curves for cassettes?
One reason is to extract the most from the tape in terms of extended treble response, minimum noise, and minimum distortion. These three desirables are conflicting; that is, an improvement in one respect necessitates a sacrifice in one or both of the others.
Proper choice of turnover frequencies, particularly the upper one, can produce an optimum compromise among the conflicting requirements.
We can look at the standard play back curves of Fig. 3 in a different light than previously: We can view them as providing treble cut above 400 Hz. The greater the descent of the curve (the greater the treble cut), the more it reduces noise in the playback portion of the tape system. Therefore, the 70-uS curve initially appears preferable to the 120-uS curve.
However, things are not that neat. As we shall explain later, the amount of bass boost (or treble cut) employed in playback governs the amount of treble boost needed in recording. The greater the bass boost in playback, the greater the treble boost needed in re cording. Thus, the 70-uS playback curve necessitates more record treble boost than does the 120-µS curve. But with increased record treble boost, there is increased risk of tape saturation, which results in distortion and impaired treble response. One could re duce the risk of tape saturation by lowering the signal level recorded on the tape, but this would reduce the signal to-noise ratio. Alternatively, one could reduce the amount of treble boost needed by lowering the amount of bias current employed in recording. How ever, less bias entails more distortion.
It is therefore necessary to look for a specific playback equalization, and thus a specific record equalization, which together permit an optimum compromise among the conflicting requirements for extended treble response, low noise, and low distortion.
The risk of tape saturation due to record treble boost varies with cassette type; hence, so does optimum playback equalization. The risk is greater for Type I cassettes than for the three other types. Therefore, the industry has taken the position-with which some disagree-that 120-uS playback equalization is optimum for Type I cassettes, and 70-uS for the other three types.
The second reason for standard playback equalization is, of course, to provide compatibility among tape decks. It is highly desirable for a cassette recorded on one deck to provide flat response when played on another.
This is possible only if all decks use the same-that is, standard-playback equalization.
We have seen that for a given cassette type there is a standard playback equalization curve. It is logical to ask whether there is also a standard record equalization curve. Strictly speaking, the answer is no. The industry standard calls for each deck to supply whatever record equalization is required to produce substantially flat response when the deck incorporates standard playback equalization; hence, a standard record curve is not needed. Moreover, it could also be troublesome. For a given cassette type, equalization supplied by the re cord amplifier tends to differ somewhat from one manufacturer's deck to another's for the following reasons:
Manufacturers may have different concepts of "substantially flat" response. Those who elect to maintain response to 20 kHz or beyond tend to use more treble boost than those who choose to go only to 16 kHz or so.
Returning to Fig. 4, we see that very substantial treble boost is needed to maintain response to 20 kHz: in this example, treble boost reaches about 17 dB at 20 kHz. But the greater the treble boost, the greater the likelihood of tape saturation, with undesirable consequences for treble response, distortion, and noise, as discussed earlier. Therefore, a manufacturer may decide to forgo flat response past 16 kHz or so in exchange for lower risk of tape saturation; accordingly, he will use less record treble boost.
The next reason has to do with width of the playback head's gap. The narrower the gap, the more extended the treble response in playback. A separate playback head can have a narrower gap, and therefore better treble response, than will a head used for both record and playback. If a deck is capable of extended playback response, it becomes desirable to extend treble boost in recording.
Record equalization will also vary with the amount of bias current each deck manufacturer uses in recording.
Bias current affects frequency response, noise, and distortion. As bias is increased, distortion is reduced, but treble response is also reduced. The reduction in treble could be offset by greater treble boost in recording, but this would increase the risk of tape saturation. Such risk could be reduced by lowering the recording level, but this would worsen the signal-to-noise ratio. Thus, the manufacturer seeks that bias current which, in his opinion, achieves an optimum compromise among the conflicting requirements for extended treble response, low noise, and low distortion. The decision as to optimum bias may differ a bit from one deck manufacturer to another; accordingly, so will the record treble boost each manufacturer uses.
Deck manufacturers choose re cord equalization with respect to a specific tape. Since tapes of the same type but of different make or variety may differ somewhat in their treble characteristics, record treble boost will also vary.
Some decks use Dolby HX Pro, which employs the high-frequency content of the audio signal as part of the total bias current. As the treble signal increases, the amount of bias current taken from the deck's bias oscillator is correspondingly reduced, to maintain a constant total bias. Such reduction in oscillator bias somewhat lessens the amount of treble boost needed.
Manufacturers may also differ in their concept of the amount of bass boost to be used in recording. We noted earlier that a slight amount of bass boost in recording is desirable to offset the leveling off of bass boost in play back from 50 Hz down. One manufacturer may elect a substantially full off set in order to maintain essentially flat record-playback response down to 20 Hz or so. Another may decide to maintain essentially flat response less far down, say to 40 or 50 Hz, and there fore will provide less bass boost in recording.
Standard Recorded Flux
Although there is no standard equalization curve with respect to the deck's record amplifier, there is an implicit standard with respect to the amount of magnetic flux (signal) recorded on the tape. As we saw in Fig. 1, if a signal were recorded flat (constant magnetic flux on the tape), the response of an ideal head (or a real head with amplifier compensation for its deviation from ideal) would rise 6 dB/octave. In this case, playback equalization would consist simply of a 6-dB/octave treble roll-off (or bass boost).
In practice, however, the playback system's equalization does not fall 6 dB/octave, but follows a standard equalization curve. This implies that the magnetic flux recorded on the tape cannot be constant if flat record-play back response is to be maintained:
Magnetic flux must be altered in accordance with the difference between a line falling at a rate of 6 dB/octave with increasing frequency (ABC in Fig. 6) and the standard playback curve (DBE).
Subtracting the standard, 70-µS playback curve (DBE) from ABC, we get curve FBG as the implicit standard recorded flux for 70-µS cassettes. For flat response to be maintained from 20 Hz to 20 kHz, recorded flux must include a bass boost that reaches about 8.5 dB at 20 Hz and a treble drop that reaches nearly 19 dB at 20 kHz.
If this treble loss is permissible (and it is, in fact, mandatory), then it is not necessary to supply enough treble boost in recording to compensate for the entire 36 dB of record losses shown for a typical cassette deck in Fig. 2. Only 17 dB of treble boost need now be supplied by the recording amplifier--and, from Fig. 4, we see that the treble boost supplied by the deck in question reaches 17 dB at 20 kHz. In keeping with the principle that recording losses should be compensated in recording, and playback losses in playback, the remaining 5 dB of the 41-dB record-play treble loss (Fig. 2) is compensated for in playback equalization (Fig. 3).
The dashed curve HBI in Fig. 6 shows the implicit standard recorded flux for Type I (120-µS) cassettes, de rived in the same manner as FBG.
We've already seen the standard play back curve for Type I, curve DBE in Fig. 3. It is significant to note that in the treble range the recorded flux for Type I cassettes is about 4.4 dB less at 20 kHz than for the other types. Therefore, less record treble boost is needed for Type I.
The reason that recorded flux is only an implicit standard is that measuring it is a difficult laboratory procedure. Therefore, standards are based on playback equalization characteristics, which are more readily measured and which, as we have just seen, imply standard recorded-flux curves.
Playback EQ and Record Treble Boost
Figure 6 has suggested that less re cord treble boost is required for Type I tapes than for the other types because of different playback equalization and, therefore, different recorded flux. Figure 7 shows specifically how choice of playback equalization, either 70- or 120-µS, affects the required amount of record treble boost for an actual cassette deck. Curve ABC repeats the unequalized record-playback response of the deck represented in Fig. 2, using Type II tape. In. Fig. 7, curve DBG shows the playback response if 70-µS playback equalization (ABC in Fig. 3) is applied to ABC. The difference between segments BI and BG is the required treble boost when 70-µS play back equalization is used. For example, at 10 kHz the playback response after playback equalization is about-9 dB. Hence, about 9 dB of treble boost is needed at 10 kHz to achieve flat record-playback response. As Figs. 4 and 5 indicate, 7 dB of this treble boost is supplied in recording, and the other 2 dB in playback.
Curve FBE in Fig. 7 shows the play back response that would result if 120-µS playback equalization were applied instead of 70-uS equalization. Less treble loss is now evident in playback so that less treble boost is needed in re cording. For example, at 10 kHz the playback response is now only about 4.75 dB down, instead of 9 dB as be fore. (To achieve utterly flat response, record equalization would have to pro duce a very slight drop, less than 1 dB at most, between approximately 500 Hz and 5 kHz.) Looking at the bass end, if 70-µS playback equalization is used, and if flat response is to be achieved, the required bass boost in recording is the difference between segments HB and DB. Such boost would reach about 5.5 dB at 20 Hz. Very similar record bass boost would be needed if 120-µS play back equalization were used instead.
(There is a seeming discrepancy: Fig. 6 indicates that, for flat response all the way down, recorded flux should be about 8.5 dB up at 20 Hz, while Fig. 7 indicates that bass boost of only about 5.5 dB is needed. However, we must recall from our discussion of Fig. 2 above that the playback head in question exhibits about 3 dB boost at 20 Hz, owing to the contour effect. This brings the required amount of record bass boost down to 5.5 dB at 20 Hz.) Figure 7 shows us something important: How the choice of playback equalization affects the required amount of record treble boost. The greater the playback bass boost, the greater must be the record treble boost. Since Type I tape cannot safely accept as much record treble boost as the other types, 120-µS playback equalization (curve DBE in Fig. 3) is used for Type I, while 70-µS playback equalization (curve ABC in Fig. 3) is reserved for the other types.
Figure 7 reveals another important fact-that the unequalized record-playback response of a deck for a given type of tape does not precisely dictate the equalization needed for essentially flat response. We see in Fig. 7 that two kinds of playback equalization could be used--either 70- or 120-µS.
By this token, other kinds could also be used, such as 90 µS, 100 uS, etc. And for each playback equalization characteristic, there would be an appropriate record treble boost.
For the purpose of illustration, Fig. 8 shows the record equalization of an actual cassette deck for Types I, II, and IV tapes. Record treble boost is significantly less for Type I, in large part because of the difference in play back equalization between Type I and the others. (The difference between Type I treble boost and that of the others reaches about 3 dB instead of the 4.4 dB that we might expect on the basis of the difference between segments BE and BG in Fig. 7. This 1.4-dB variance is due to the different characteristics of the various tapes for which the deck in question is adjusted.)
The difference between the ideal head's output (DBE) and curve ABC represents the equalization which the playback system must actually supply. Compare curve ABC of Fig. 3.
A Controversy About Type II EQ
Some in the industry have questioned whether 70-µS playback equalization is the wisest choice for Type II tape. They would prefer a curve with an appreciably higher time constant than 70 µS, such as 120 µS. In other words, they would like less bass boost in playback and, therefore, less treble boost in recording. The greater treble boost entailed in 70-uS equalization affords less recording headroom--i.e., less protection against tape saturation and its concomitant distortion and treble loss. They cite the increasing abundance of program material with strong high-frequency content, particularly on Compact Discs and premium phono discs, and the resultant need for adequate headroom. They would be willing to give up several dB of S/N (better with 70-uS equalization) in exchange for several dB more headroom (better with 120-uS equalization).
The controversy may be settled by continuing advances in the state of the art. Modern noise-reduction systems principally Dolby C and dbx-afford signal-to-noise ratios in the 70- and 80-dB range. The recordist blessed with such S/N and seeking to avoid tape saturation can afford to lower the re cording level several dB-say, by about 4.5 dB, which is the maximum difference between the record treble boost entailed in 70- and 120-uS equalization-and still have a very good signal-to-noise ratio. Developments such as Dolby HX Pro and the Dolby C treble recording characteristic reduce the risk of tape saturation.
Confusion About Playback EQ
Until about 1965, the industry ex pressed standard playback equalization in terms of the frequency contour the playback system should supply primarily a bass-boost curve, as shown straightforwardly in Fig. 3. However, since 1965, playback EQ has been ex pressed in terms of the deck's desired output when playing a tape which produces constant flux in the core of the playback head at all frequencies, as shown in Fig. 9. Thus, the actual equalization is not curve ABC of Fig. 9, but the difference between this curve and the output of an ideal head (the 6-dB/ octave slope of curve DBE). A graph of this difference would reproduce curve ABC of Fig. 3.
Effectively, the curve labeled "required playback EQ" in Fig. 9 is the inverse of that in Fig. 3, tilted to reflect the fact that it is referenced to a 6-dB/ octave slope instead of the horizontal line of flat response. This has led to a frequent misunderstanding-that playback equalization consists largely of treble boost instead of bass boost.
Many readers have inquired .about the effects of using equalization set tings other than those normally recommended for specific tape types. The most obvious effects are slight alterations of treble response when play back and record equalization are mis matched. If a tape intended for 70-µS playback is played back with 120-uS EQ, a slight treble boost will be heard.
If a recording intended for 120-µS playback is played back with 70-uS EQ, there will be a slight treble cut. In theory, this cut or boost will reach 4.4 dB at 20 kHz, as shown in Fig. 10.
In practice, however, the difference may be more on the order of 2.5 to 3 dB, as indicated by the record equalization curves of Fig. 8. The differences between actual and theoretical treble response could be explained in terms of differences in actual equalization curves supplied by the deck in question, or differences in the treble response and saturation characteristics of various tape formulations, especially if the tape in use is not the tape which the deck manufacturer used in adjusting record equalization characteristics.
What if Type I tape were both re corded and played back with Type II or IV equalization, or Type II or IV tape were recorded and played back with Type I EQ? In each case, the treble changes in recording would just about balance those in playback, so overall record-playback response would be only slightly affected.
However, we must keep in mind that signal-to-noise ratio would always be affected, with 70-uS playback equalization producing less noise (higher S/N). After all, that is the reason for using 70-uS instead of 120-uS play back equalization.
It should further be kept in mind that use of Type II or IV record equalization with a Type I tape will increase the risk of tape saturation, and therefore of distortion and loss of extreme treble, unless the recordist deliberately reduces the recording level by several dB.
How Open-Reel Decks Compare
To round out the discussion of our subject, let's compare open-reel tape deck equalization with cassette equalization. Standard playback equalization for open-reel decks follows the five basic principles listed near the beginning of this article. The playback curves for open-reel look much the same as for cassette, save for differences in the upper turnover frequency and reduced need for playback treble boost to compensate for playback-head losses. In all cases, the lower turnover frequency remains 50 Hz (3,180 uS). For speeds of 1 7/8, 3 3/4, 7 1/2 and 15 ips, there are official standards for conventional (ferric oxide) tape and de facto standards for EE (extra efficiency-akin to Type II) tape.
As stated earlier, record and treble losses become less severe as tape speed is increased. Therefore, less re cord treble boost is needed at higher speeds in order to achieve a given amount of recorded magnetic flux. Or, for the same treble boost as before, one can achieve more recorded flux; this in turn entails greater playback bass boost, with a consequent improvement in signal-to-noise ratio (see Fig. 6 for the relationship between playback bass boost and recorded flux). In practice, the upper turnover frequency is chosen to afford some of each of the advantages gained from higher tape speed: Somewhat less treble boost, reducing the risk of tape saturation, and somewhat more play back bass boost, resulting in a higher signal-to-noise ratio.
Both for cassette and open-reel decks, and for the various speeds and tape types commonly used, Table I shows the upper turnover frequencies of the standard playback curves. It also shows, for each curve, the total amount of equalization (bass boost) from frequencies above 20 kHz down to below 20 Hz. Total bass boost (equalization) is given by 20 log (f2 divided by f1), where f2 is the upper turnover frequency and f1 is the lower turnover frequency. If you want to calculate the amount of bass boost at a given frequency, use this equation:
where Bf is bass boost at the frequency of interest, f is frequency of interest, f1 is the lower turnover frequency (al ways 50 Hz), and f2 is the upper turn over frequency.
For example, assume we want to know the bass boost at 1 kHz for the playback equalization curve with time constants of 70 and 3,180 µS. First we convert time constants into turnover frequencies by dividing the constants into 159,155 so that f1 equals 50 Hz and f2 equals 2,274 Hz. Then:
If you wish to use 400 Hz as the 0-dB reference, calculate the boost for 400 Hz and subtract this from the boost for the frequency of interest, yielding B'f.
For example, 8400 equals 15.2 dB; subtracting 15.2 dB from 7.9 dB shows that 6'1000 equals-7.3 dB when 400 Hz is the 0-dB reference. That is, the equalization curve at 1 kHz is 7.3 dB below its level at 400 Hz.
The principles of tape equalization, and their implementation in cassette decks, are complex. Luckily for the tape user, however, one can make excellent recordings without grasping these principles in detail. It is necessary only to grasp the deck's equalization switch, and set it to match the tape that is being used.
Table I--Upper turnover frequencies and total bass boost for standard playback curves. The lower turnover frequency is 50 Hz (3,180 µS) in all cases.
(adapted from Audio magazine, Jun. 1985)
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