How Important is Tape Azimuth? (Sept. 1984)

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Not least among the factors that enable a cassette system to maintain essentially flat response out to 15 kHz or more is accurate azimuth alignment of its record and playback head or heads. A considerable number of queries received by my "Tape Guide" column grow out of the problem of achieving and maintaining such accuracy.

above: An error of 20', or one third of a degree, (see text). Click image for full-size view.

Azimuth refers to the orientation of the head gap with respect to the direction of tape motion. To simplify discussion, we'll temporarily assume that a tape head has but one gap (rather than the two needed for stereo). In the absolute sense, correct azimuth alignment denotes that the gap of a tape head is perfectly perpendicular to the direction in which the tape moves, as in Fig. 1. If not, we can say there is absolute azimuth error, depicted by the angle in Fig. 2; for clarity, the angle is greatly exaggerated.

Absolute azimuth error may be caused by the head being mounted with its gap slantwise to the tape path or by the tape skewing with respect to the gap when in motion, as in Fig. 3.

Such error tends to produce increasing loss of signal as frequency rises (Fig. 4); we can call this azimuth loss. The loss occurs not on the tape but in playback.

Whether azimuth loss does occur depends on relative azimuth error-on the azimuth of the playback head relative to the azimuth of the record head.

For compatibility among tape decks, it is desirable that both heads be correctly aligned in the absolute sense, as in Fig. 1; therefore, both will then have the same azimuth, so that relative azimuth error is nonexistent.

However, if absolute azimuth error does exist, but is the same in both the record and playback heads, the errors cancel; there will be no relative azimuth error and no azimuth loss.

Thus, it is advantageous to have a two-head deck, so that the same head is used for record and playback. Even though the head may not be in absolute azimuth alignment, the errors in record and playback will tend to cancel, and there tends to be little or no azimuth loss when playing a tape recorded with that head. (The possibility of some azimuth loss, usually slight, still exists because, depending on the quality of the cassette and of the deck, the tape might skew differently in recording than in playback, resulting in relative azimuth error.) Significant azimuth loss can more easily happen with a three-head deck, one which employs separate heads for record and playback. Such loss occurs still more easily when different decks are used to record and playback, as with borrowed, traded, and commercially prerecorded cassettes and those tapes recorded on a formerly owned deck.

In summary, it is relative azimuth error which concerns us (although this does not diminish the importance of absolute azimuth alignment to insure compatibility among decks). Hereafter I will simply say azimuth error to denote relative error. Also for simplicity, I will assume that azimuth is absolutely correct in recording, with error occurring only in playback; after all, it isn't until playback that the consequence of azimuth error was manifest.

Azimuth Loss and Tape Format

We have already noted that azimuth loss increases as frequency rises. The loss also increases as tape speed is reduced. (Both causes of increased loss are really different sides of the same coin: The loss increases as the wavelength decreases-and wave length, which is speed divided by frequency, grows shorter as frequency rises or as speed drops.) Because of this, the azimuth problem is more acute at the cassette speed of 1 7/8 ips than at the speeds of 3 3/4 and 7 1/2 ips commonly used in home open-reel decks.

On the other hand, azimuth loss de creases as track width is narrowed. So the cassette's narrower track (0.024 inch, versus 0.043 inch on four-track open-reel tape) partially offsets the effect of its lower speed as compared to open-reel tape (Table I). But the azimuth problem still remains greater for cassette systems.

Azimuth error angles of less than 1° can produce disastrous treble loss.

Therefore, since the angles we deal with are very small, they are usually not stated in degrees but in minutes (60ths of a degree)-for example, 12' instead of 0.2°. From Table I, we see that an azimuth error of only 12' (0.2°) produces a possibly acceptable loss of 3.07 dB at 10 kHz and a truly unacceptable loss of 7.77 dB at 15 kHz. Greater azimuth errors produce losses far out of keeping with the concept of high fidelity. (It should be recognized that the losses in Table I are additional to treble losses caused by other factors in a tape system, such as tape saturation, electrical characteristics of tape heads, insufficiently narrow gap in the playback head, improper equalization in recording or playback, tape properties, etc.)

For a cassette system to maintain fairly good response out to 15 kHz, Table I indicates that the azimuth error angle, a, must be kept under 9'; for good response out to 20 kHz, alpha = 6' is at the edge of acceptability. Preferably, alpha should be kept to no more than about 3', which produces a loss of less than 1 dB at 20 kHz.

It may be of interest to visualize how small the values of a under discussion are, and thus appreciate the care that must be exercised by deck and cassette makers and by others in dealing with the azimuth problem. To do so, the following takes .only a few moments. Assume a gross, totally unacceptable error of 20' (or one-third degree). On an 8 1/2 x 11-inch sheet of blank paper, draw a light, thin vertical line down the middle from top to bottom, with Points A and B respectively designating top and bottom of the line.

One-sixteenth inch to the right of Point B, mark Point C. Connect Points A and C with a light, thin line. Lines AB and AC will now form an angle of 20'. Darken line AC for 1-13/16 inch, starting from the top, and designate the bottom of the darkened line as Point D. If AB corresponds to tape width (0.150 inch), AD corresponds to the upper gap of the head of a cassette deck (0.024-inch long). Although we know that AD deviates from vertical, our eye cannot detect the deviation. Clearly, azimuth alignment by eye is out of the question. (On the other hand, some people can do a fairly good job of aligning the playback head by ear, using a tape containing program material with substantial high frequency content or using an azimuth alignment tape containing a high frequency.) It is clear from Table I that open-reel tape, with its higher speeds, can tolerate greater azimuth error than cassette, despite the cassette's narrower track. This is especially true of 7 1/2-ips open-reel format. For example, Table I shows that an azimuth error angle of 6' is at the edge of acceptability (down 3 dB at 20 kHz) for cassette, while with 7 1/2-ips open-reel tape, a 12' error is within the edge. Looking at Table I from another point of view, we see that, for a given azimuth error, 7 1/2-ips open reel tape suffers much less treble loss than the 1 7/8-ips cassette.

At 3 3/4 ips, however, the azimuth problem is only slightly less for open reel than for cassette. The advantage of faster speed is nearly cancelled by the disadvantage of greater track width. Hence 6' azimuth error is approximately at the edge of acceptability for both formats; Table I shows that such error produces a loss of 3.07 dB at 20 kHz for cassette, and a loss of 2.42 dB at 20 kHz for 3.75-ips open reel tape.

Fig. 1--Correct absolute azimuth.

Fig. 2--Absolute azimuth error (exaggerated, for clarity) due to head misalignment.

Table I--Playback loss (in dB) due to azimuth error in common home tape systems.

In the past, a few cassette decks have incorporated 3 3/4 ips as an extra speed for improved fidelity. One of the improvements is greatly reduced azimuth loss. For example, an azimuth error of 9' produces only 1.67 dB of loss at 20 kHz with a tape speed of 3 3/4 ips, compared with 7.77 dB of loss at 1 7/8 ips. For cassette, the edge of acceptability goes from about 6' at 1 7/8 ips to about 12' at 3 3/4 ips.

The azimuth problem becomes all the more pronounced in two slow-speed tape systems, not yet discussed here, that have become part of the audio scene: 1 7/8-ips open-reel and 15/16-ips cassette. To illustrate, assume an azimuth error of 6', which is at or within the edge of acceptability for other systems discussed thus far. This would produce losses of 2.42 and 5.95 dB respectively at 10 and 15 kHz in a 1 7/8-ips open-reel system, and of 3.07 and 7.77 dB in a 15/16-ips cassette system. Such losses are unacceptable for high fidelity.

General Principles

If we stay within the area of "moderate" losses-say, not exceeding about 10 or 12 dB-we may infer from Table I and other data that square-law principles apply (in approximate fashion) to azimuth loss. Azimuth loss increases roughly as the square of any increase in angle of azimuth error, frequency or track width, and as the square of any decrease in tape speed. In other words, if you double the azimuth error angle, the recorded frequency or the track width, the loss in output will quadruple; if you double the tape speed, the azimuth loss will diminish to one-fourth of its original value.

In the area above "moderate" azimuth losses (say above 10 or 12 dB), the square-law principles give way to losses that move precipitously toward infinite as azimuth error increases, frequency rises, tape speed declines, and track width increases.

The table and other data also show that maximum acceptable azimuth error tends to decrease in proportion to any decrease in tape speed or increase in track width. To illustrate, maximum acceptable azimuth error tends to be halved if tape speed is halved or if track width is doubled.

The Colinearity Problem

For simplicity, Figs. 1, 2, and 3 show only one head gap. But cassette tape heads ordinarily have two, one for each stereo channel. Each gap is about 0.024 inch long, and the two are spaced about 0.011 inch apart. Ideally, they should be colinear, that is, both in the same straight line, so that if one is correctly aligned for azimuth the other is too.

However, depending on the quality of the head, the gaps may depart from colinearity, as shown in Fig. 5 (greatly exaggerated, there, for clarity). In such circumstances, the optimum alignment is that yielding equal azimuth loss in each channel.

Calculating Azimuth Loss

When azimuth error is stated (in an equipment review or elsewhere), it is given either as an angle (a) or as phase shift (P) at a specified frequency. If one has a pocket calculator with trigonometric and logarithmic functions, the following equations enable one to readily translate a into azimuth loss or P into α.

(Common track widths are 0.043 inch for quarter-track open-reel, 0.024 inch for stereo cassette. The 180 and pi factors convert degrees into radians, the "20 log" term converts the answer to dB.)

To illustrate, assume that azimuth error a = 0.1° (or 6'), and we wish to know the azimuth loss at 15,000 Hz for cassette. In this case, F = 15,000, W = 0.024, tan a = 0.0017453, and S = 1.875.

Therefore, T = (0.017453 x 15,000 x 0.024) 1.875 = 0.3351032, so that

(Note that the answer appears as a negative, signifying a signal loss.) To convert phase error into azimuth error requires a different formula:

Fig. 3--Tape skew can effectively misalign a head positioned properly with relation to the tape deck. The effective alignment that results (A) is at an angle to the tape; repositioning the head produces corrected alignment (B).

Fig. 4--Loss vs. frequency, as a function of azimuth error, for cassette tape.

Fig. 5--Noncolinear head gaps (greatly exaggerated).


Compatibility in Tape Decks


It would seem that if the same alignment tape were used to adjust the playback heads on several three head tape decks, and then each re cord head was adjusted for an exact match to its respective playback head, the recorded flux would have the same orientation to the tape on each deck.

We might further conclude that a tape made with flat response on one deck could be replayed with flat response on a second deck.

Unfortunately, the situation is more complex than indicated. To get data on what really happens, I used a BASF Type II Alignment Tape to adjust the playback heads of three decks, all with separate record and playback head gaps. Two of these, the Nakamichi 582 and Tandberg TCD 3014, had separate record and playback head assemblies. The third, an Aiwa AD-M700, had a single head with separate record and playback gaps. In the Aiwa deck, therefore, the position of the record-head azimuth was automatically determined by the playback alignment with the test tape.

In the first tests, I made a recording of pink noise on the Tandberg TCD 3014 using Maxell XL II-S at 20 dB below Dolby level after the record head had been adjusted for the best response. The playback on the TCD 3014 was displayed and stored with a 1/2-octave real-time analyzer (Fig. 1, top). This same tape was then played back on the Nakamichi 582 (middle) and the Aiwa AD-M700 (bottom). All of the playback responses are quite flat over most of the range, but there are differences. The response on the Tandberg, which recorded the tape (top), is the flattest-as would be expected. The Nakamichi 582 playback (middle), however, displays a rising output above 2 kHz or so, which raises a question I'll answer a bit later. The response on the Aiwa AD-M700 deck would be considered disappointing, particularly in comparison with the other two decks. Immediately, it might be concluded that there was considerable alignment error, even though the ADM700's head had been adjusted using the same test tape.

The second set of tests used the Nakamichi 582 as the recording deck, with a change to TDK SA-X tape, just to see if the tape skewing characteristics of a different cassette would affect the results. Figure 2 shows the very flat response at 20 dB with playback on the 582 deck (top). With playback on the Tandberg TCD 3014 (middle), however, the high-frequency rolloff is quite evident. The drooping response with the Aiwa deck is quite similar to that in the earlier figure, with a dB or so more rolloff.

(left) Fig. 1--Playback responses with recording made on Tandberg TCD 3014 cassette deck. Top, Tandberg; middle, Nakamichi 582; bottom, Aiwa AD-M700. (Vertical scale: 5 dB/div.); (right) Fig. 2--Playback responses with recording made on Nakamichi 582. Top, Nakamichi; middle, Tandberg TCD 3014; bottom, Aiwa AD-M700. (Vertical scale: 5 dB/div.)

(left) Fig. 3--Playback responses with recording made on Aiwa AD-M700. Top, Aiwa; middle, Nakamichi 582; bottom, Tandberg TCD 3014. (Vertical scale: 5 dB/div.); (right) Fig. 4--Misalignment and jitter with 5-kHz test tone. Top, playback of reference track A on recording Nakamichi 582; middle, playback of trace B of 582, illustrating relative jitter; bottom, playback of same tape on Tandberg TCD 3014, showing alignment shift and jitter of track B relative to track A of TCD 3014. See text. (Horizontal scale: 30°/div.)

Before drawing any conclusions, I ran a similar test set using the Aiwa AD-M700 as the recording deck, using XLII-S. The response in playback on the Aiwa deck is quite flat overall. The 8-dB drop at 20 kHz is a characteristic of this medium-performance deck.

Playing this tape, the response on the Nakamichi 582 (middle) showed a rise above 1 kHz, while that on the Tandberg TCD 3014 (bottom) showed closer correspondence to the Aiwa deck results. Note that there is some vertical broadening of the 12.5-, 16- and 20 kHz filter-level indications for both the 582 and the TCD 3014-especially the 582. A separate check showed that the effect was caused by slight skewing of the tape on the Aiwa during recording.

Because of the very short distance between the record and playback gaps of the Aiwa combination head, there were no skew-caused level variations in its playback.

An examination of the responses in Figs. 1 to 3 along with some analysis, including reference to past experience, led me to these conclusions: (1) The playback equalization of the Nakamichi 582 is relatively elevated at the higher frequencies compared to that of the Tandberg TCD 3014; (2) The playback equalization and/or head response of the Aiwa AD-M700 rolls off compared to both of the other decks; (3) The Aiwa deck uses "extra" record equalization to compensate for the roll-off in playback, and (4) The alignment match between decks adjusted with the same alignment tape was fairly good, despite the equalization-caused response differences which might make things appear otherwise.

In confirmation of what some readers are already thinking, I must state that the playback equalization (70 µS for Type II), as given mathematically in international standards, is not followed exactly by the great majority of manufacturers. I won't take up space here to discuss the whole issue, but it can be noted that the Nakamichi playback is close to that for an ideal head, while the Tandberg's is closer to that for the IEC reference playback head.

Figures 1 and 2 reflect this relationship, with the Nakamichi recording rolled off on the Tandberg, and the Tandberg recording boosted on the Nakamichi. These response differences relate to equalization and not to azimuth error. Figure 4 illustrates what azimuth error might be found between these two decks. I recorded a 5-kHz tone on the Nakamichi 582, both tracks. In the playback, track A (top) was the 'scope sweep reference, and the broadening of the track B trace (middle) shows the jitter of B versus A. There was some amplitude variation on both tracks. The average position of its trace shows that B lags A by about 6° at 5 kHz, with 30° of total jitter. The phase error of 6° is equivalent to an alignment error of less than 1 minute of arc. The bottom trace is that of track-B playback of the same tape on the TCD 3014, with the 'scope locked to its track A. Here the jitter is higher, and B leads A by 20°, still just 2 minutes of alignment difference. So, a final word: Align heads carefully, but be aware of possible equalization discrepancies between decks.


(The distance between centerlines of the stereo tracks is 0.035 inch for cassette and 0.125 for quarter-track open reel.) To illustrate, an Audio review of a top-notch cassette deck stated that phase error measured 15° at a test frequency of 12,500 Hz. Thus P = 15, S = 1.875, D = 0.035, F = 12,500, so that

α = arc sin [15 x 1.875 / 360 x 0.035 x 12,500]

= arc sin 0.0001786

= 0.0102 degrees (or 0.61 minutes)

So small an azimuth error would cause very minute azimuth loss, for example merely 0.03 dB loss at 20,000 Hz.

How Azimuth Loss Occurs

Assume that a sine-wave signal is recorded at 1 7/8 ips on cassette tape. The recorded signal is equivalent to a series of bar magnets end to end, as in Fig. 6--north poles adjacent to north poles, and south poles to south poles.

Each bar represents a half wavelength, and its poles correspond to the positive and negative peaks of the half wavelength. The higher the frequency, the shorter are the bar magnets because more of them must fit into each inch of tape. At the upper end of the treble range, say above 10,000 Hz, they become extremely short, on the order of less than 0.0001 inch. (At 10,000 Hz, a half-wavelength = 1.875/ 20,000 = 0.0000938 inch.)

At any given instant of playback, each edge of the head's gap contacts a given intensity and polarity of magnetic field produced by the bar magnets. Because the two gap edges contact different parts of a bar or of adjacent bars, most of the time each edge is at a different field intensity. Therefore most of the time a magnetic potential exists between the two edges. The potential constantly changes in intensity and polarity as the gap traverses the bar magnets, and the changing potential induces a voltage in the coil of the playback head.

As frequency rises and the bars become shorter, the difference in field intensity and polarity at the two edges of the gap increases, thereby increasing head output. Maximum output occurs when the distance between gap edges equals a half wavelength (one bar), with one gap edge contacting a north pole while the other contacts a south pole, resulting in maximum potential across the gap. Output falls rapidly as frequency increases further, reaching zero when an entire wavelength equals the distance across the head gap, since the potential will then always be equal at each gap edge.

Hence, the importance of a very narrow playback gap for extended high frequency response.

The greater the field intensity seen by each gap edge, the greater can be the magnetic potential between edges at various instants, and the greater can be the changes in potential, thus increasing head output. Contrariwise, if anything reduces the field intensity seen by the gap edges, this reduces head output.

Fig. 6--How azimuth loss occurs: Recorded signals are essentially bar magnets of varying length. Head output depends on the difference in magnetic field bridged by the head gap-a difference greatly reduced when the gap is tilted to bridge areas of different flux.

Azimuth error performs such a reduction. When there is no azimuth error, in playback all parts of the left edge are in contact with the same polarity and intensity of magnetic field.

That is, the upper and lower sections of the edge see the same field intensity as the center of the edge. But azimuth error tilts the edge with respect to the magnetic bar, so that the central, upper, and lower sections contact different magnetic intensities, which partially cancel each other. The same is true, of course, for the right edge.

To help visualize this, assume that the center of a gap edge is at the north pole of a bar magnet and thus sees maximum field intensity. But if the edge tilts, its top and bottom sections are no longer at the north pole and therefore are at points of reduced intensity. Accordingly the intensity seen by the edge as a whole is reduced.

This process doesn't work in reverse; that is, tilting the gap edge doesn't increase the field intensity seen by it. To illustrate, assume that the center of the edge is at the middle of a bar, where intensity is minimum.

Now the top and bottom of the edge do see higher intensities than does the center of the edge. But the top and bottom incline in opposite directions, toward opposite polarities, so that these higher intensities cancel each other and leave the edge as a whole at minimum intensity.

Considering how short are the bar magnets at high frequencies, very slight gap tilt (azimuth error) will cause the top and bottom of a gap edge to ride very different field intensities, with substantial cancelling effect. To illustrate, assume a cassette player with an azimuth error of 9', tilting the top of an edge to the left and the bottom to the right. Therefore the bottom of the edge is displaced 0.000063 inch to the right with respect to the top of the edge.

(Displacement = sin a x gap length = 0.002618 x 0.024 inch = 0.000063 inch.)

Next assume a frequency of 15,000 Hz, so that a half-wavelength, or one magnetic bar, = 1.875/30,000 = 0.000063 inch.

Now assume that the center of the gap edge contacts a bar's north pole, where field intensity is maximum. Because the tilted edge in our example spans an entire magnetic bar, the top and bottom of the edge must be at midpoints of magnetic bars, where field intensity is minimal. Thus, the field intensity seen by the gap edge as a whole is quite substantially reduced.

At lower frequencies, where the recorded magnetic bars are longer, a given gap tilt causes the top and bottom of a gap edge to be displaced only a fraction of a bar relative to the center of the edge. Therefore the cancelling effect on field intensity seen by the edge is reduced, and azimuth loss is less.

The above discussion paves the way to our understanding why, for a given azimuth error and tape speed, the azimuth loss increases with track width.

As the track width, and therefore gap height, is increased, the top and bottom of the tilted gap edge are displaced a greater distance along the tape path from the center of the gap.

To illustrate: We noted earlier that at 1.875 ips an azimuth error of 9' results in a displacement of the edge bottom relative to the edge top of 0.000063 inch when track width is 0.024 inch (cassette). When track width is 0.043 inch (open-reel), the displacement increases to 0.00011 inch. As already noted, the greater the displacement, the greater is the reduction in field intensity seen by the gap edge as a whole, increasing azimuth loss.

Minimizing Azimuth Error

From the foregoing it is obvious that great care must be exercised by all parties to the tape recording process in order to minimize azimuth error.

The cassette deck manufacturer must pay close attention to proper azimuth alignment of the head or heads used for recording and playback. This requires an accurate test tape on which a high frequency, such as 10,000 Hz, has been recorded with the gap of the record head (in the deck that produces the tape) exactly at a 90° angle relative to the direction of tape travel. The playback or record playback head of the deck being aligned is then oriented for maximum output from the test tape. If the deck being aligned has a separate record head, it is adjusted, while recording and monitoring a high-frequency signal, for maximum output from the previously aligned playback head.

If head gaps are not colinear, so that correct alignment of one gap necessitates azimuth error of the other, an optimum position has to be found that achieves equal azimuth loss in both stereo channels. If there are separate heads for record and playback, optimization becomes more complex. And it is even more complex in the case of reversible decks which use heads with four gaps.

Production of an accurate azimuth alignment tape is not an easy matter and requires precise laboratory procedures. Even for test tapes made by companies of high reputation, it has been noted that somewhat different results may be obtained from tapes of different companies. However, these differences tend to be slight and are becoming slighter as new azimuth alignment tapes appear.

Care must be exercised by the deck manufacturer to properly adjust tape tension and thereby minimize tape slewing (a change in the angle of the tape with respect to the head). Toward the same end, the cassette deck must be designed so that the cassette is uniformly and securely locked in place.

Equal care applies to the cassette itself. It may appear to be a disarmingly simply affair but it is really a very sophisticated device that must be built with a high degree of precision in order to operate properly. Guides must be accurate and true, and the tape must be slit very accurately, in order to minimize slewing.

Reverse cassette operation presents an extra azimuth problem because the tape tends to slew differently when running from left to right than from right to left. One solution is to use a head with two gaps instead of four and rotate the heads 180°, with a separate azimuth adjustment (a stop screw) for each direction. Another solution is to turn the cassette over, as one turns the page of this magazine, so that the tape always runs in the same direction with respect to the heads. A third solution, used in the Nakamichi Dragon, is to continuously adjust the playback head azimuth during operation. This is achieved by dividing the gap for one of the playback tracks into two sections; as a tape is played, the phase difference between gap sections is constantly monitored, and azimuth is adjusted by a motor to minimize the phase difference and thereby minimize azimuth loss.

(adapted from Audio magazine, Sept. 1984)

Also see:

The Whys and Hows of Cassette Equalization (Jun. 1985)

History of Magnetic Recording—part 2 (Sept. 1984)

The March of Technology: Analog Tape Home Recording (May 1997)

Understanding Equalization and Time Constants (Feb. 1982)

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