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Characteristics of current film heads
Journal of Magnetism North-Holland
and Magnetic Materials 94 (1991) 197-206
Characteristics
197
of current film heads
Yuh Tyng Huang Material Research Laboratory
ITRI, Hsinchy
Taiwan
and Huei Li Huang Department
of Physics, National Taiwan University,
Taipei, Taiwan
Received 6 August 1990; in revised form 26 September 1990
Gap-nulls appear in the reproducing spectrum in any symmetric inductive head. This poses severe limitations to the application of inductive heads in high density reading processes. However, based on the equivalence of the current thin film sheet to a Karlqvist head in generating magnetic fields and the principle of linear superposition, stacked current thin film sheets, discrete or continuous, can both effectively smooth out the gap-nulls in their respective spectral response curves up to very large k-values. These types of reading heads can be either an asymmetric stack of thin film sheets flushing with one side or a continuoous bulk current film head in a trapezoidal cross section, and are capable of resolving a bit density of 50 Mbpi without producing any gap-nulls.
1. Introdnction
A few years back it was suggested [l] that a thick, non-parallel single pole head was able to produce frequency characteristics which was gapnull free and monotonous in the high density region for perpendicular recording. The paper presented only heuristic arguments, however, and treated the accounts only qualitatively. Later, a seperate paper [2] showed that two infinitely long current carrying strips placed between two highly permeable regions can make it possible to prepare an inductive head without gap-nulls possible. Hereby, we presented a third type of gap-null free inductive head [3] which is based simply on the principle of linear superposition and the fact that a two dimensional current carrying thin film sheet of width g, carrying current 2NI ampere turns, is 0304-8853/91/$03.50
equivalent to a Karlqvist head carrying NI ampere turns with a gap length g. This makes the superposition of the reading heads physically realizable. Briefly stated, by placing a stack of thin film sheets flushing with one side, it was possible to generate a spectral response function whose gapnulls tend to be smoothed out by means of superposition if the sheet widths are properly arranged and separated or, if it is a continous film, a properly assymmetrized trapezoidal thin film. There are similarities and differences among the references cited above. For example, both refs. [1,3] are trapezoidal in shape but the former is made of magnetic material, while the latter is of conducting film. Further characteristics of the current film heads such as effects of geometries, gap-null cancellation behaviour and the phase angle variations, etc., will be elaborated as follows.
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
Y.T. Huang H.L.. Hung
198
/ Characteristics of current film hea&
that there is no relative phase angle variation vs. for this type of symmetric heads.
2. Symmetric stack of current thin films
k
The longitudinal component of field due to the nth current sheet [4] (see fig. 1) is I
3. Asymmetric stack of current thin films
dn)/2+x tan Y(“> -Y [ -1
f&(x, Y) = y$q
dn)/Q-x Y(n)-Y
+tan-’
0)
1.
Thus, the head’s reproducing spectral function is V(k)
1 v sin(kidn)/2) a T 1 eCkdcn) k(n)/2 0 n=l
’
(2)
where d(n)=d+y(n)=d+(n-1) Ad is the spacing of the nth sheet from the medium, g(n) and Z, is, respectively, the width and current of the n th sheet, and k = 27/X is the wave number, N is the total number of sheets and 1, is the total current. For simplicity, the sheet width is assumed to vary linearly, g(n) = Kg(N) - g(I))/(N l)]( n - 1). The term sin( kg/2)/( kg/2) is the typical gap-null loss factor, which comes from the Fourier transform of the head field. Presently, we will focus on whether or not the gap-null response can be smoothed out for a given configuration. To this end, factors such as media thickness losses, etc., that have not been figured importantly in the calculations, are ignored in the discussions to follows. Note that the reality of eq. (2) assures us
Consider an asymmetric stack of current thin film sheets flushing with the left margin, as shown in fig. 2. Otherwise, the notations are not different from the above. The readout voltage spectral function is V(k)
e-ikg(n)/2
kg(n)/2
0 n=l
(3) The last factor in eq. (3), eeikg(“)/‘, representing the phase response from the n th sheet, comes from the Fourier transform of the head field as a result of the shifted origin shown in fig. 2. A different sheet width gives rise to nulls at different values of k, that is, different wavelengths. It is anticipated that an appropriate arrangement of linearly varying sheet width shall result in evenly separated gap-nulls at correspondingly separated k-values. Consequently, the gap-nulls are expected to be smoothed out based on the principle of linear superposition. The overall phase angle response behaviour vs. k can be easily obtained from eq. (3). We have, phase angle B(k) = tan-‘(Im V(k)/Re V(k)), in which Re
v
1 N ~inbd~b’21 a T c eCkdcn)
V(k)
=
5
Re
V,(k)
n=l
T.
Q(n), In I
(da) Im V(k) =
E
Im
V,(k)
n=l
Fig. 1. Configuration
of a symmetric stack of current carrying thin films sheets.
= _
n$le-kd(n)
‘ln
i:[;)‘2
sin
!%$!!I.(4b)
Y. T. Huang, H. L Huang / Characteristics
4. Asymmetric
e-kd a MY)
dY
For the trapezoidal head we consider also a geometric variation of the form
=do) + [g(t) -dON(Y/~)”
in which n = 1 is an authentic trapezoid with linear non-parallel edges. For n equal to other integers (> 1) or fractional number ( < l), we have a distorted trapezoid with shrinked (concave) or bloated (convex) edges. Typical geometries of these
u
medium Fig. 2. Configuration
(4
1 d
‘“‘” ‘“‘L/
Fig. 3. Configuration of a bulk current film head in trapezoidal forms. (a) Linear trapezoid; (b) convex trapezoid; (c) concave trapezoid.
(5)
g(v)
199
bulk current film heads: trapezoidal
Next, consider the case in which Ad -+ 0, N + co, and the current is uniform throughout. We then have a bulk current film head with a trapezoidal cross section, as shown in fig. 3a. For this configuration we let t be the thickness, I,, be the total current, of the trapezoid. It is, thus, equivalent to a stack of a infinite number of current film sheets each with an infinitesimally small thickness dy, width g(y), fed with current &g(y) dy/jdg(y) dy, located between y and y + dy. Similar to eq. (2) the spectral response of this configuration can be rewritten in an integral form
V(k)
of current film headv
>
movement
of an asymmetric stack of current carrying thin film sheets.
heads are shown in fig. 3b and c. Consequences these geometries are discussed as follows.
of
5. Results and discussions As an illustration, consider gap-nulls from a typical symmetric stack of thin films with N = 2, g, = 0.3 pm, g, = 0.5 pm, interspacing Ad = 0.02 pm, as follows. Gap-nulls from each sheet show up at k = 20.9, 41.9, 62.8 (l/pm), etc., for g,; and at 12.6, 25.1, 37.7, 50.3 (l/pm), etc., for g,. Thus, for k falling in the range of 20.9 > k > 12.6, etc., the readout voltage from each sheet bears opposite signs. As a consequence, the gap-nulls remain intact, though shallower and displaced to k = 18, or at X = 2~/18 pm, and so on. Fig. 4 shows the well known spectral response curve for N = 5 with the sheet widths: 0.3, 0.35, 0.4, 0.45 and 0.5 l.trn. If N is further increased, the essential features of the response curve remain mostly unchanged, with the exception that the signal level is relatively reduced due to the enhanced spacing loss factor. For an asymmetric stack of current thin films flushed with one side, the situation is different. Fig. 5 shows the reproduced spectrum for N = 2, with g, = 0.3 pm, g, = 0.5 pm. Following eq. (4), the
200
Y. T. Huang
H. L. Huang
/ Characteristics
of current
film heads
Fig. 4. Spectral response curve for a symmetric stack of thin films. N = 5, g(l) = 0.3, g(5) = 0.5, d = 0, Ad = 0.02, all in pm
reproduced voltage is a complex quantity. The real part of it has its first null at about k = 9 (l/pm), and the rest of nulls at other k-values down the line. The imaginary part, on the other hand, never vanishes, except at very large k-values. As a result, the gap-nulls are largely compensated, while some shallow dips remain. Figs. 6a and b reflect succinctly the situation and the result of calculations. When N = 3, the spectral curve is practically smooothed out, as shown. As N increases further,
the smoothness of the curve does not seem to have improved. On the contrary, traces of the residual effect of gap-nulls reappear with increasing N. These features including the cases for N equals to 3, 5 and 8 are shown in fig. 7. Fig. 8 shows a comparison of the spectral responses from a trapezoidal head vs. a Karlquist’s head. The smooth, gap-nulls free, curve is from a trapezoidal head with g(0) = 0.3 pm, g(t) = 0.6 pm, t = 0.1 pm, d = 0.15 pm. The curve is visibly
Fig. 5. Spectral response curve for an asymmetric stack of thin films. N = 2, g(l) = 0.3, g(2) = 0.5, d = 0, Ad = 0.02, all in pm.
Y. T. Huang, H. L. Huang / Characteristics
smoother in comparison with those of the asymmetric stack of thin films shown in fig. 7. It appears that the thinner the bulk film, the smoother the curve. This seems strongly substantiated by the results shown in fig. 9, in which the top and the bottom width of the trapezoid varies from 0.3 to 0.7 pm. A similar and a bit smoother spectral curve has been obtained also for the width varying from 0.3 to 0.8 pm, and so on. This implies that this trapezoid film head is capable of responding to the bit length b I 0.10 pm without
..............
201
producing gap-nulls in the spectral response curve. Note well that thinness alone is not sufficient to guarantee smoothness of the curves, unless the the slope of the non-parallel edge is reasonably slow. In other words, a smooth spectral response curve can be assured only if the gap-nulls, of all orders and periods, resulted from each infinitesimal sheet width are uniformly spread out. Any grouping of gap-nulls will inevitably lead to incomplete gapnulls cancellation, hence the residual nulls, as suggested in fig. 10 and reflected earlier in fig. 7.
..!............... 20
k:(Vkd Fig. 6. Decomposition
of current film headr
a
of spectral response function for an asymmetric stack of thin film sheets corresponding (b) imaginary part.
to fig. 5. (a) Real part;
Y. T. Huang, H. L. Hunng / Characteristics
202
Fig. 7. Comparison
of spectral
response
curves for an asymmetric stack of thin film sheets. g(l) = 0.3, g(N) all in pm, and N = 3.5 and 8.
0
T
20
I
k:
Fig. 8. Spectral
response
= 0.5, d = 0, Ad = 0.02,
effect of the bottom (broader) width, but the curve smoothes out at larger k-values. By contrast, the latter shows residual nulls corresponding to the weighted effect of the top (narrower) width, and does not seem to show sign of smoothing out. If higher order of gap-nulls can be carefully arranged to spreadout evenly to achieve smooth spectral response curves, as in fig. lla, it may serve good
Thus, the smoothness of the spectral response depends sensitively on the slope of the non-parallel edge of the trapezoid. Fig. lla shows spectral curves for convex trapezoids (fig. 3b) corresponding to n = 1, l/3, l/5 in eq. (6), and fig. llb shows the same for concave trapezoids (fig. 3c) for n = 1, 3, 5. The former reveals residual nulls due to the added
-140 t-.
of current film heads
40 (
f
thd
curve for a trapezoidal head. g(0) = 0.3, g(t) = 0.6, t = 0.1, d = 0.15, all in pm. Curve with gap-nulls a Karlqvist’ head with g = 0.45 pm, d = 0.15 pm.
is for
Y. T. Huang, H. L. Huang / Characteristics
Fig. 9. Spectral
response
curves for trapezoidal
heads.
= 1V(k)
1eieCk).
(7)
For a symmetric head, the phase angle can be either a linear function of k if it is not symmetri-
Fig. 10. Spectral
response
curves
203
g(0) = 0.3, g(t) = 0.7, t = 0.05, 0.1, 0.15, and d = 0.15, all in pm.
purposes as high density reading heads, just as n = 1 trapezoids does with linear, non-parallel edges. The phase angle for the spectral response function, 8(k), can in general be expressed as V(k)
of current film heads
tally positioned with respect to the coordinate system, zero if it is. If a head is asymmetric, such as those shown in Figs. 3, 8(k) can be a complicated function of geomentry. Fig. 12 show a series of curves describing undulatory behaviour of the phase angles variation as a function of k. The amplitude of the phase angle undulation falls roughly within the ranges of 60 to 140 O. The smoother the head’s spectral response curve gets,
for trapezoidal heads. g(0) = 0.3, g(t) = 0.5, t = 0.05, 0.1, 0.2, and d = 0.15, all in pm. Note the residual nulls, despite the films are so thin.
Y. T. Huang, H. L. Huang / Characteristics
204
the smaller the undulation amplitude becomes. For example, fig. 12a, which has appreciable undulation, corresponds to an asymmetric stacking of thin films and one of the curves with visible residual nulls shown in fig. 7 in which g(1) = 0.3, g(N) = 0.5, N = 5, all in pm. Fig. 12b, whose phase response curve is a bit smoother than the preceding one, corresponds to a smoother spectral curve shown in fig. 8 for a trapezoidal head: g(0) =0.3 pm, g(t) =0.6 pm, t =O.l pm. Fig. 12d is related to a trapezoidal head with g(0) = 0.3 pm, g(t)=02 urn, t=0.05 pm, which has a
..... .. ;
n
-
-:
7t
:
mDe.‘lee
:
7&
of current film heads
spectral response curve smoother than shown in fig. 9. It is rightly expected that a smooth spectral response curve should be closely correlated to a smooth, flat phase response curve. Finally, it should be remarked that the H, component of field and its field gradient related to fig. 12d does not seem very sharp, as shown in fig. 13. The halfwidth of the field gradient distribution is about 0.3 pm, corresponding to a moderate bit density of approximately 50 Mbpi. It seems that sharpness of the head field gradient is not a prerequisite to produce a smooth spectral response
= =
a
-1404
0
T
40
20 k
(
t
f/wd
Fig. 11. Spectral response curves for trapezoidal heads. g(0) = 0.3, g(t) = 0.6, t = 0.1, d = 0.15, all in pm. (a) Convex trapezoids, with n = 1, l/3 and l/5; (b) concave trapezoids, with n = 1, 3 and 5 (see text for the definition of n).
Y. T. Huang, H.L.. Huang / Characteristics
curve, contrary to remarks made elsewhere for ring heads [S]. The above statements hold for current film heads, but not necessarily for ring or thin film heads, since the latter generate a head field which deviates substantiallly from Karlqvist’s
of current film heads
205
field at low spacings [6]. The effect of the head field on the gap-nulls remains to be evaluated. Based on the characteristics features described above, it is clear that an asymmetric stack of current thin film heads, a thin trapezoid with
Fig. 12. Variation of the phase response curves from different type of film heads. (a) Asymmetric stack of thin films; g(1) = 0.3, g(N) =0.5, all in pm, N= 5; (b) Linear trapezoid; with g(0) = 0.3, g(r) = 0.6, t =O.l, all in pm; (c) Linear trapezoid; with g(0) = 0.3, g(r) = 0.6, 1= 0.05, all in pm; (d) Linear trapezoid; with g(0) = 0.3, g(r) = 0.8, I = 0.05, all in pm.
206
Y. T. Huang, H. L. Huang / Characteristics 20000
of current film heads
-J
=0.3-0.8/&m /ii f=O.OS m ! y-O.1 &pm :
i
Fig. 13. Distribution of the H, component of field and its field gradient for a trapezoid corresponding to fig. 12d.
non-parallel edge in particular, are capable of generating smooth spectral response curves. Since the H, and H, components of the field are simply related through its Fourier transform by H,,(k, y) = j H,( k, y), regardless of the head geometry or magnetization patterns [7], the same head is equally suited for use in both longitudinal and perpendicular reading modes.
6. Summary In this paper, we studied mainly the behaviour of two types of reproducing heads: 1) an asymmetric stack of properly arranged current carrying thin film sheets flushing with one side; 2) a trapezoidal bulk current film head. For heads which display a symmetric head field distribution, gap-nulls are ubiquitous and appear at equal spacings. For the two types of heads discussed above, however, both the gap-nulls and their residual effects can be effectively smoothed out. The extent of the smoothness of the spectral curve depends sensitively on the slope of the non-parallel edge of the film head, in addition to the film thickness. Combining figs. 9 and 13, trapezoidal current film
heads serving as reading heads are capable of linear density corresponding to a bit length b = 0.30 urn without producing gap-nulls in both longitudinal and perpendicular recording.
Acknowledgement This research is supported in part by the National Science Council of Taiwan.
References [l] A. Ohtsubo and Y. Satoh, IEEE Trans. Magn. MAG-18 (1982) 1173. [2] M.J. Vos and J. Judy, IEEE Trans. Magn. MAG-24 (1988) 2401. [3] Y.T. Huang, C.R. Chang and H.L. Huang, paper CA-5, presented at INTERMAG’90, Brighton, UK. [4] 0. Karlqvist, Trans. Royal. Inst. Techn. Stockholm (1954) 86. [5] C.S. Wang and H.L. Huang, paper presented at INTERMAG-90, Brighton, UK; see also ref. [2]. [6] H.L. Huang and H.Y. Deng, IEEE Trans. Magn. MAG-22 (1986) 1305. [7] J.C. Mallinson, IEEE Trans. Magn. MAG-10 (1974) 773.
and Magnetic Materials 94 (1991) 197-206
Characteristics
197
of current film heads
Yuh Tyng Huang Material Research Laboratory
ITRI, Hsinchy
Taiwan
and Huei Li Huang Department
of Physics, National Taiwan University,
Taipei, Taiwan
Received 6 August 1990; in revised form 26 September 1990
Gap-nulls appear in the reproducing spectrum in any symmetric inductive head. This poses severe limitations to the application of inductive heads in high density reading processes. However, based on the equivalence of the current thin film sheet to a Karlqvist head in generating magnetic fields and the principle of linear superposition, stacked current thin film sheets, discrete or continuous, can both effectively smooth out the gap-nulls in their respective spectral response curves up to very large k-values. These types of reading heads can be either an asymmetric stack of thin film sheets flushing with one side or a continuoous bulk current film head in a trapezoidal cross section, and are capable of resolving a bit density of 50 Mbpi without producing any gap-nulls.
1. Introdnction
A few years back it was suggested [l] that a thick, non-parallel single pole head was able to produce frequency characteristics which was gapnull free and monotonous in the high density region for perpendicular recording. The paper presented only heuristic arguments, however, and treated the accounts only qualitatively. Later, a seperate paper [2] showed that two infinitely long current carrying strips placed between two highly permeable regions can make it possible to prepare an inductive head without gap-nulls possible. Hereby, we presented a third type of gap-null free inductive head [3] which is based simply on the principle of linear superposition and the fact that a two dimensional current carrying thin film sheet of width g, carrying current 2NI ampere turns, is 0304-8853/91/$03.50
equivalent to a Karlqvist head carrying NI ampere turns with a gap length g. This makes the superposition of the reading heads physically realizable. Briefly stated, by placing a stack of thin film sheets flushing with one side, it was possible to generate a spectral response function whose gapnulls tend to be smoothed out by means of superposition if the sheet widths are properly arranged and separated or, if it is a continous film, a properly assymmetrized trapezoidal thin film. There are similarities and differences among the references cited above. For example, both refs. [1,3] are trapezoidal in shape but the former is made of magnetic material, while the latter is of conducting film. Further characteristics of the current film heads such as effects of geometries, gap-null cancellation behaviour and the phase angle variations, etc., will be elaborated as follows.
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
Y.T. Huang H.L.. Hung
198
/ Characteristics of current film hea&
that there is no relative phase angle variation vs. for this type of symmetric heads.
2. Symmetric stack of current thin films
k
The longitudinal component of field due to the nth current sheet [4] (see fig. 1) is I
3. Asymmetric stack of current thin films
dn)/2+x tan Y(“> -Y [ -1
f&(x, Y) = y$q
dn)/Q-x Y(n)-Y
+tan-’
0)
1.
Thus, the head’s reproducing spectral function is V(k)
1 v sin(kidn)/2) a T 1 eCkdcn) k(n)/2 0 n=l
’
(2)
where d(n)=d+y(n)=d+(n-1) Ad is the spacing of the nth sheet from the medium, g(n) and Z, is, respectively, the width and current of the n th sheet, and k = 27/X is the wave number, N is the total number of sheets and 1, is the total current. For simplicity, the sheet width is assumed to vary linearly, g(n) = Kg(N) - g(I))/(N l)]( n - 1). The term sin( kg/2)/( kg/2) is the typical gap-null loss factor, which comes from the Fourier transform of the head field. Presently, we will focus on whether or not the gap-null response can be smoothed out for a given configuration. To this end, factors such as media thickness losses, etc., that have not been figured importantly in the calculations, are ignored in the discussions to follows. Note that the reality of eq. (2) assures us
Consider an asymmetric stack of current thin film sheets flushing with the left margin, as shown in fig. 2. Otherwise, the notations are not different from the above. The readout voltage spectral function is V(k)
e-ikg(n)/2
kg(n)/2
0 n=l
(3) The last factor in eq. (3), eeikg(“)/‘, representing the phase response from the n th sheet, comes from the Fourier transform of the head field as a result of the shifted origin shown in fig. 2. A different sheet width gives rise to nulls at different values of k, that is, different wavelengths. It is anticipated that an appropriate arrangement of linearly varying sheet width shall result in evenly separated gap-nulls at correspondingly separated k-values. Consequently, the gap-nulls are expected to be smoothed out based on the principle of linear superposition. The overall phase angle response behaviour vs. k can be easily obtained from eq. (3). We have, phase angle B(k) = tan-‘(Im V(k)/Re V(k)), in which Re
v
1 N ~inbd~b’21 a T c eCkdcn)
V(k)
=
5
Re
V,(k)
n=l
T.
Q(n), In I
(da) Im V(k) =
E
Im
V,(k)
n=l
Fig. 1. Configuration
of a symmetric stack of current carrying thin films sheets.
= _
n$le-kd(n)
‘ln
i:[;)‘2
sin
!%$!!I.(4b)
Y. T. Huang, H. L Huang / Characteristics
4. Asymmetric
e-kd a MY)
dY
For the trapezoidal head we consider also a geometric variation of the form
=do) + [g(t) -dON(Y/~)”
in which n = 1 is an authentic trapezoid with linear non-parallel edges. For n equal to other integers (> 1) or fractional number ( < l), we have a distorted trapezoid with shrinked (concave) or bloated (convex) edges. Typical geometries of these
u
medium Fig. 2. Configuration
(4
1 d
‘“‘” ‘“‘L/
Fig. 3. Configuration of a bulk current film head in trapezoidal forms. (a) Linear trapezoid; (b) convex trapezoid; (c) concave trapezoid.
(5)
g(v)
199
bulk current film heads: trapezoidal
Next, consider the case in which Ad -+ 0, N + co, and the current is uniform throughout. We then have a bulk current film head with a trapezoidal cross section, as shown in fig. 3a. For this configuration we let t be the thickness, I,, be the total current, of the trapezoid. It is, thus, equivalent to a stack of a infinite number of current film sheets each with an infinitesimally small thickness dy, width g(y), fed with current &g(y) dy/jdg(y) dy, located between y and y + dy. Similar to eq. (2) the spectral response of this configuration can be rewritten in an integral form
V(k)
of current film headv
>
movement
of an asymmetric stack of current carrying thin film sheets.
heads are shown in fig. 3b and c. Consequences these geometries are discussed as follows.
of
5. Results and discussions As an illustration, consider gap-nulls from a typical symmetric stack of thin films with N = 2, g, = 0.3 pm, g, = 0.5 pm, interspacing Ad = 0.02 pm, as follows. Gap-nulls from each sheet show up at k = 20.9, 41.9, 62.8 (l/pm), etc., for g,; and at 12.6, 25.1, 37.7, 50.3 (l/pm), etc., for g,. Thus, for k falling in the range of 20.9 > k > 12.6, etc., the readout voltage from each sheet bears opposite signs. As a consequence, the gap-nulls remain intact, though shallower and displaced to k = 18, or at X = 2~/18 pm, and so on. Fig. 4 shows the well known spectral response curve for N = 5 with the sheet widths: 0.3, 0.35, 0.4, 0.45 and 0.5 l.trn. If N is further increased, the essential features of the response curve remain mostly unchanged, with the exception that the signal level is relatively reduced due to the enhanced spacing loss factor. For an asymmetric stack of current thin films flushed with one side, the situation is different. Fig. 5 shows the reproduced spectrum for N = 2, with g, = 0.3 pm, g, = 0.5 pm. Following eq. (4), the
200
Y. T. Huang
H. L. Huang
/ Characteristics
of current
film heads
Fig. 4. Spectral response curve for a symmetric stack of thin films. N = 5, g(l) = 0.3, g(5) = 0.5, d = 0, Ad = 0.02, all in pm
reproduced voltage is a complex quantity. The real part of it has its first null at about k = 9 (l/pm), and the rest of nulls at other k-values down the line. The imaginary part, on the other hand, never vanishes, except at very large k-values. As a result, the gap-nulls are largely compensated, while some shallow dips remain. Figs. 6a and b reflect succinctly the situation and the result of calculations. When N = 3, the spectral curve is practically smooothed out, as shown. As N increases further,
the smoothness of the curve does not seem to have improved. On the contrary, traces of the residual effect of gap-nulls reappear with increasing N. These features including the cases for N equals to 3, 5 and 8 are shown in fig. 7. Fig. 8 shows a comparison of the spectral responses from a trapezoidal head vs. a Karlquist’s head. The smooth, gap-nulls free, curve is from a trapezoidal head with g(0) = 0.3 pm, g(t) = 0.6 pm, t = 0.1 pm, d = 0.15 pm. The curve is visibly
Fig. 5. Spectral response curve for an asymmetric stack of thin films. N = 2, g(l) = 0.3, g(2) = 0.5, d = 0, Ad = 0.02, all in pm.
Y. T. Huang, H. L. Huang / Characteristics
smoother in comparison with those of the asymmetric stack of thin films shown in fig. 7. It appears that the thinner the bulk film, the smoother the curve. This seems strongly substantiated by the results shown in fig. 9, in which the top and the bottom width of the trapezoid varies from 0.3 to 0.7 pm. A similar and a bit smoother spectral curve has been obtained also for the width varying from 0.3 to 0.8 pm, and so on. This implies that this trapezoid film head is capable of responding to the bit length b I 0.10 pm without
..............
201
producing gap-nulls in the spectral response curve. Note well that thinness alone is not sufficient to guarantee smoothness of the curves, unless the the slope of the non-parallel edge is reasonably slow. In other words, a smooth spectral response curve can be assured only if the gap-nulls, of all orders and periods, resulted from each infinitesimal sheet width are uniformly spread out. Any grouping of gap-nulls will inevitably lead to incomplete gapnulls cancellation, hence the residual nulls, as suggested in fig. 10 and reflected earlier in fig. 7.
..!............... 20
k:(Vkd Fig. 6. Decomposition
of current film headr
a
of spectral response function for an asymmetric stack of thin film sheets corresponding (b) imaginary part.
to fig. 5. (a) Real part;
Y. T. Huang, H. L. Hunng / Characteristics
202
Fig. 7. Comparison
of spectral
response
curves for an asymmetric stack of thin film sheets. g(l) = 0.3, g(N) all in pm, and N = 3.5 and 8.
0
T
20
I
k:
Fig. 8. Spectral
response
= 0.5, d = 0, Ad = 0.02,
effect of the bottom (broader) width, but the curve smoothes out at larger k-values. By contrast, the latter shows residual nulls corresponding to the weighted effect of the top (narrower) width, and does not seem to show sign of smoothing out. If higher order of gap-nulls can be carefully arranged to spreadout evenly to achieve smooth spectral response curves, as in fig. lla, it may serve good
Thus, the smoothness of the spectral response depends sensitively on the slope of the non-parallel edge of the trapezoid. Fig. lla shows spectral curves for convex trapezoids (fig. 3b) corresponding to n = 1, l/3, l/5 in eq. (6), and fig. llb shows the same for concave trapezoids (fig. 3c) for n = 1, 3, 5. The former reveals residual nulls due to the added
-140 t-.
of current film heads
40 (
f
thd
curve for a trapezoidal head. g(0) = 0.3, g(t) = 0.6, t = 0.1, d = 0.15, all in pm. Curve with gap-nulls a Karlqvist’ head with g = 0.45 pm, d = 0.15 pm.
is for
Y. T. Huang, H. L. Huang / Characteristics
Fig. 9. Spectral
response
curves for trapezoidal
heads.
= 1V(k)
1eieCk).
(7)
For a symmetric head, the phase angle can be either a linear function of k if it is not symmetri-
Fig. 10. Spectral
response
curves
203
g(0) = 0.3, g(t) = 0.7, t = 0.05, 0.1, 0.15, and d = 0.15, all in pm.
purposes as high density reading heads, just as n = 1 trapezoids does with linear, non-parallel edges. The phase angle for the spectral response function, 8(k), can in general be expressed as V(k)
of current film heads
tally positioned with respect to the coordinate system, zero if it is. If a head is asymmetric, such as those shown in Figs. 3, 8(k) can be a complicated function of geomentry. Fig. 12 show a series of curves describing undulatory behaviour of the phase angles variation as a function of k. The amplitude of the phase angle undulation falls roughly within the ranges of 60 to 140 O. The smoother the head’s spectral response curve gets,
for trapezoidal heads. g(0) = 0.3, g(t) = 0.5, t = 0.05, 0.1, 0.2, and d = 0.15, all in pm. Note the residual nulls, despite the films are so thin.
Y. T. Huang, H. L. Huang / Characteristics
204
the smaller the undulation amplitude becomes. For example, fig. 12a, which has appreciable undulation, corresponds to an asymmetric stacking of thin films and one of the curves with visible residual nulls shown in fig. 7 in which g(1) = 0.3, g(N) = 0.5, N = 5, all in pm. Fig. 12b, whose phase response curve is a bit smoother than the preceding one, corresponds to a smoother spectral curve shown in fig. 8 for a trapezoidal head: g(0) =0.3 pm, g(t) =0.6 pm, t =O.l pm. Fig. 12d is related to a trapezoidal head with g(0) = 0.3 pm, g(t)=02 urn, t=0.05 pm, which has a
..... .. ;
n
-
-:
7t
:
mDe.‘lee
:
7&
of current film heads
spectral response curve smoother than shown in fig. 9. It is rightly expected that a smooth spectral response curve should be closely correlated to a smooth, flat phase response curve. Finally, it should be remarked that the H, component of field and its field gradient related to fig. 12d does not seem very sharp, as shown in fig. 13. The halfwidth of the field gradient distribution is about 0.3 pm, corresponding to a moderate bit density of approximately 50 Mbpi. It seems that sharpness of the head field gradient is not a prerequisite to produce a smooth spectral response
= =
a
-1404
0
T
40
20 k
(
t
f/wd
Fig. 11. Spectral response curves for trapezoidal heads. g(0) = 0.3, g(t) = 0.6, t = 0.1, d = 0.15, all in pm. (a) Convex trapezoids, with n = 1, l/3 and l/5; (b) concave trapezoids, with n = 1, 3 and 5 (see text for the definition of n).
Y. T. Huang, H.L.. Huang / Characteristics
curve, contrary to remarks made elsewhere for ring heads [S]. The above statements hold for current film heads, but not necessarily for ring or thin film heads, since the latter generate a head field which deviates substantiallly from Karlqvist’s
of current film heads
205
field at low spacings [6]. The effect of the head field on the gap-nulls remains to be evaluated. Based on the characteristics features described above, it is clear that an asymmetric stack of current thin film heads, a thin trapezoid with
Fig. 12. Variation of the phase response curves from different type of film heads. (a) Asymmetric stack of thin films; g(1) = 0.3, g(N) =0.5, all in pm, N= 5; (b) Linear trapezoid; with g(0) = 0.3, g(r) = 0.6, t =O.l, all in pm; (c) Linear trapezoid; with g(0) = 0.3, g(r) = 0.6, 1= 0.05, all in pm; (d) Linear trapezoid; with g(0) = 0.3, g(r) = 0.8, I = 0.05, all in pm.
206
Y. T. Huang, H. L. Huang / Characteristics 20000
of current film heads
-J
=0.3-0.8/&m /ii f=O.OS m ! y-O.1 &pm :
i
Fig. 13. Distribution of the H, component of field and its field gradient for a trapezoid corresponding to fig. 12d.
non-parallel edge in particular, are capable of generating smooth spectral response curves. Since the H, and H, components of the field are simply related through its Fourier transform by H,,(k, y) = j H,( k, y), regardless of the head geometry or magnetization patterns [7], the same head is equally suited for use in both longitudinal and perpendicular reading modes.
6. Summary In this paper, we studied mainly the behaviour of two types of reproducing heads: 1) an asymmetric stack of properly arranged current carrying thin film sheets flushing with one side; 2) a trapezoidal bulk current film head. For heads which display a symmetric head field distribution, gap-nulls are ubiquitous and appear at equal spacings. For the two types of heads discussed above, however, both the gap-nulls and their residual effects can be effectively smoothed out. The extent of the smoothness of the spectral curve depends sensitively on the slope of the non-parallel edge of the film head, in addition to the film thickness. Combining figs. 9 and 13, trapezoidal current film
heads serving as reading heads are capable of linear density corresponding to a bit length b = 0.30 urn without producing gap-nulls in both longitudinal and perpendicular recording.
Acknowledgement This research is supported in part by the National Science Council of Taiwan.
References [l] A. Ohtsubo and Y. Satoh, IEEE Trans. Magn. MAG-18 (1982) 1173. [2] M.J. Vos and J. Judy, IEEE Trans. Magn. MAG-24 (1988) 2401. [3] Y.T. Huang, C.R. Chang and H.L. Huang, paper CA-5, presented at INTERMAG’90, Brighton, UK. [4] 0. Karlqvist, Trans. Royal. Inst. Techn. Stockholm (1954) 86. [5] C.S. Wang and H.L. Huang, paper presented at INTERMAG-90, Brighton, UK; see also ref. [2]. [6] H.L. Huang and H.Y. Deng, IEEE Trans. Magn. MAG-22 (1986) 1305. [7] J.C. Mallinson, IEEE Trans. Magn. MAG-10 (1974) 773.