Parent Category: 2019 HFE

*By Kenneth S. Schneider*

**Ed. Note: Part one of this article published in the June 2019 issue of High Frequency Electronics.**

Considering Figures 3 a-d it is evident that with respect to frequency, “f,” |ELFEXT (f, X)| dB can be partitioned into 4 segments- a Low Frequency Segment, an Intermediate Frequency Segment, a High Frequency Segment and Very High Frequency Segment. The Low Frequency Segment extends from 0 Hz to FL MHz- This exact boundary is somewhat arbitrary and loosely dependent upon the length “X.” However, it is approximately 1 MHz. It is typically characterized at short lengths- e.g. 66 m- by the presence of some resonant notches and ripples and at higher lengths by continuous convex curvature. The derivative of |ELFEXT (f, X )| dB with respect of “f” in the Low Frequency segment is certainly not constant but if it were to be “roughly” approximated it would be 10 dB per decade. The crosstalk mechanism in this segment is probably a combination of both capacitive and inductive coupling. The Intermediate Frequency Segment extends from FL MHz up to a boundary frequency of FI MHz. This boundary frequency depends “loosely on the length, “X.” It can be approximated-for the range of lengths of interest here- at 60 MHz. Again, the derivative of |ELFEXT (f, X) |with respect of “f” in the Intermediate Frequency segment is not constant. It tends to be high at the low end of this frequency range but “then settles out” and can be well approximated by 20 dB per decade for most of this segment. It is this behavior which has been modelled in [3]. This behavior indicates that capacitive coupling dominates as the cause of the crosstalk coupling in this frequency range. The High Frequency Segment extends from FI MHz to FH MHz. Again, the boundary frequency FH MHz depends “loosely” on the length “X”- decreasing with increasing “X.” It varies from about 100 MHz to 200 MHz for the lengths of interest in the model. It can be approximated by 150 MHz. The derivative of |ELFEXT (f, X)| dB with respect of “f” in the High Frequency segment is certainly not constant but “close” to it though slowly increasing. It can be well approximated by 40 dB per decade for most of this segment. Though this “exact” value is somewhat arbitrary and just indicates a significant “slope discontinuity” in the “straight line approximations” to these segments. The Intermediate Frequency Segment and the High Frequency Segment illustrate what has been referred to as the “Dual Slope Effect.” But, as is evident from these figures this is a very simplistic-if not crude- way of describing what is clearly a very complex phenomenon. Computational experiments performed in the modelling indicate that this “slope discontinuity” is directly related to the frequency dependence of the conductivity and to the presence of the periodic twists in the cables. There are “ripples” evident at the lower lengths see for example the region between 100 MHz and 200 MHz for 66 m are due to the periodic twists as has been made clear from computational experiments. These seem to move to the high frequencies with greater loop lengths. All of this indicates a very complex interaction of different coupling mechanisms. These most likely include capacitive coupling, inductive coupling complicated by the twisting. The Very High Frequency Segment begins at F_{H} MHz and extends upward from that to 1 GHz and beyond. Here |ELFEXT (f, X) | dB versus “f” appears to “oscillate” in an aperiodic manner often going well above 0 dB. The oscillations seem to follow the pattern like a “downward Chirp Radar waveform-with a frequency parameter rather than a time parameter- and with a decreasing amplitude. However, this “extreme” aperiodicity is a “little deceptive” as the abscissa is logarithmic. Studies performed in developing the model indicate that this is principally caused by the aperiodic twists and to a much lesser extent by the increase in the imaginary component of the dielectric constant. Notice at the extreme right-hand side of each of the figures- close to 1 GHz. This behavior seems “to burst out again.” Computations indicate that this is “roughly” repetitive in with increasing frequency. The presence of this behavior with |ELFEXT| repeatedly going through 0 dB may well affect the cancellation of FEXT through Vectoring- which is a key processing technique used in the development of the emerging broadband technologies. Furthermore, the oscillatory, behavior is like paired echo distortion. If it gives rise to “early” and “late” echoes of the FEXT this may also affect the cancellation of FEXT through Vectoring- there may be loss of synchronization of the FEXT with the direct path signals.

Figure 3 • |ELFEXT (f, X) | dB vs frequency in Hz for a. X = 66 m, b: X = 100 m, c: X= 200 m, d: 400 m.

Clearly from considering Figure 3 a-d FL, FI and FH vary “loosely” with loop length. But, for the purposes of the continued development of the model herein they are approximated as follows:

F_{L} ≈ 1 MHz., F_{I} ≈ 60 MHz.

F_{H} ≈ 150 MHz(16)

Discussion now will be directed at the variation-of |ELFEXT (f, X)| dB with “X” at different fixed frequencies, “f.” This is illustrated by Figure 4 which covers the range of lengths which are of interest in the emerging broadband communication technologies—i.e. up to several 100 m. This is also shown for a wide range of fixed frequencies ranging from 1 MHz to 100 MHz. The range of frequencies has been limited to be less than FH MHz – the beginning of the “Very High Frequency Segment”- because variation with respect to “X” with the oscillatory behavior is really not meaningful.

Considering Figure 4, and the computational analyses underlying it indicates that at the lower lengths, “X” there is almost a linear dependence of |ELFEXT| on “X” and therefore a logarithmic dependence of |ELFEXT| dB on “X.” However, as “X” increases this logarithmic dependence of |ELFEXT| dB on “X” gives way to |ELFEXT| dB approaching a fixed asymptote- the value of which depends upon the fixed frequency. Figure 4 indicates that “the neighborhood” of this asymptote is reached generally when “X” is in the interval from 400 m to 500 m.

Figure 4 • |ELFEXT (f, X) |dB in dB versus X in meters for different fixed frequencies (LEFT)

Figure 5 • |ELFEXT (f, X) |dB in dB versus X in meters or a fixed frequency of 50 MHz and different twist lengths (RIGHT)

The almost linear dependence upon X at the lower values of “X” has been observed and expected at communication technologies which have been of interest, in the past, at the lower frequencies-below 30 MHz. It is usually readily explained as follows. If the transmission line model is considered from the point of view of “Circuit Theory” with the crosstalk effected by capacitive coupling -the dominant mechanism at these frequencies- then what you have are a continuing number of capacitors in parallel- increase with “X.” As “X” increases the number of capacitors increases and the FEXT would be expected to grow linearly with “X.” This has been noted in the technical literature. The great Bell Telephone Laboratories engineer, G. A. Campbell noted this in the application to the twisted pair cable loops of the telephone system [8]. Work on similar but different problems has also noted this [9], [10], [11] though not in the context of twists in the cable.

Now what is very interesting in observing Figure 4 is that the “linear dependence”- (logarithmic in dB)- “disappears.” The variation with “X” instead appears to follow the linear dependence up to some threshold length, “X_{0}, “- in the 400 m to 500 m interval-and the for lengths X > X_{0} rapidly approaches an asymptote.” This asymptotic behavior is consistent with the modelling approach obtained through simulations and reported by van den Brink [4] and extended by van den Brink, H. Verbueken, J. Maes. For purposes of continuing the modelling in the sequel the following specification will be made:

X_{0} = 400 m(17)

Computational experiments have been carried out with the model being developed which appear to indicate that this deviation of the dependence of |ELFEXT| dB on “X” from logarithmic to asymptotic behavior is related to the length of the twist in the Quad Cable. Figure 5 illustrates this and indicates |ELFEXT| dB versus “X” at a fixed frequency of 50 MHz for 3 different twist lengths. Note that as the twist length gets shorter and shorter then tendency to deviate from the logarithmic behavior to the asymptotic behavior gets more pronounced

The characteristics which have been noted in the above discussion allow the following formulae to be used as a reasonable approximation to |ELFEXT (f, X) |dB which can be used for further modelling and simulation purposes. These formulae follow the trend lines indicated and for simplicity do not include the resonant effects- except for the Very High Frequency segment where the oscillatory behavior has been represented.

|ELFEXT (f, X) | dB ≈ [ KFEXT] dB + Γx [f, X] dB + Γf (f, X) dB(18)

Here Γx [ X] dB principally represents the dependence upon “X” and is defined by:

Γx [f, X] dB = 20Log [X] for X ≤ X_{0}

Γx [f, X] dB = 20 Log [X_{0}] for X > X_{0} (19)

where X_{0} is given by (17).

Γf (f, X) | dB principally represents the dependence upon “f” and is given below with FL, FI and FH given by (16):

**Low Frequency Segment**

Γf (f, X) dB = 10 Log (f) for f ≤ FL(20)

**Intermediate Frequency Segment**

Γf (f, X) dB = Γ (FL, X) dB + 20 Log (f) for FL.< f ≤ FI(21)

Where the first term on the right-hand side comes from (19)

**High Frequency Segment**

Γf (f, X) dB = Γ (FL, X) dB + 40 Log (f) for FI.< f ≤ FH(22)

Where the first terms on the right-hand side comes from (21).

**Very High Frequency Segment**

Γf (f, X) dB = Γ (FH, X) dB + AΓ (f ) sin (2 π f λΓ ) for f > FH .

Where AΓ = 40 e – (fM- 150)/100 and λΓ = 4 (23)

[ KFEXT] dB = -165.6505(24)

The value of [ KFEXT] _{dB} corresponds to K_{FEXT} = 5.59 x 10-9. This is higher than the value used in [3] which is 8.80 x 10 ^{-11}. However, a difference is to be expected as [3] deals with unshielded twisted pair cables and the current modelling effort is directed at Quad Cables. As noted the above formulas are approximations. They are a simplification of quite complex behavior- this is especially true with respect to the specifications of AΓ and λΓ . The intent was to put in these in a form so that they can be readily applied in simulation efforts. However, they do capture the characterizations observed from the exact computational results.

Consideration is now given to the phase Φik (f, X) with respect to “X” and “f.” “Φik (f, X)” has not received adequate attention in modelling efforts directed at other cable types such as those presented in [3] and [6]. van den Brink does discuss it for Quad Cable in [4]- though quite tersely.

“Φik (f, X)” has been computed using the analytical approach of the mathematical development which is the basis of the model presented. Figure 6 a, b, c, d, and e illustrate Φik (f, X) (degrees) vs. frequency (Hz) for a range of exposure lengths “X.”

Figure 6 • “Φik (f, X)” vs. “f” for different exposure lengths, “X,” a. 66 m, b. 100 m, c. 200 m, d. 300 m, e. 400 m.

In considering the examples of the phase variation with frequency shown in Figure 6 they all have similar characteristics. The phase variation appears constant at an average value of approximately -50 degrees up until about the beginning to the Very High Frequency Segment- slightly above 100 MHz. At this point it becomes oscillatory- very similar to the |ELFEXT| dB behavior. Note again that the abscissa in Figure 6 is in logarithmic units and this deceptively makes the variation look like a decreasing period- yet this behavior is interesting. It indicates that in this Very High Frequency Segment the phase seems to oscillate between approximately 180 degrees and -180 degrees. Though this again may be deceptive because -180 degrees is effectively 180 degrees and once could say that the phase is at 180 degrees. The origin of this behavior in the Very High Frequency Segment is a subject for future study.

**“****θ****ik****“**

This parameter has been addressed for the case of Binders of Unshielded Twisted Pair cable using a novel statistical approach in [3]. However, this required the collection of a massive amount of experimental data to estimate the underlying statistical distribution. Such data is currently not available for the case of interest here-dealing with Quad Cables. With the development of the present model focused on Quad Cables a deterministic “geometric approach” is employed. It should be noted that Strobel also used a geometric approach as reported in Appendix I of [7]- which though not readily evident does have some similarities.

figure 7 • Diamond based grid (LEFT)

Figure 8 • Placement of individual Quad Cables on the diamond grid (RIGHT)

The geometric approach used herein rests on 3 assumptions which will be justified. However, it must be noted that this approach follows that of [3] in ignoring any frequency dependence of “θik. “This is a necessary simplification as it is beyond the range of issues addressed by the modelling effort presented. **Assumption #1**- Initially all Quads are close packed with each Quad located on the lattice points of a diamond shaped grid. Such a grid is illustrated in Figure 7. The coordinates of the lower boundary are (1,0) … (1,15). The coordinates of the left boundary are (0,1) …(0,14). The coordinates of other points can be discerned from this. The diamond shaped grid is used because its symmetry mirrors the symmetry of a Quad and this is convenient for descriptive purposes.

The placement of individual Quad Cables on such a diamond grid is illustrated in Figure 8. Here 4 cables are shown. The location of each Quad is the coordinate of its center point. Thus, the location of Q-1 is the coordinate (1,1). The location of Q-2 is (2,2). Other Quad Cables will be so identified. It is to be noted that in Figure 3 the 2 Quad Cables, Q-1 and Q-2 are “adjacent”-they are as close as possible.

A configuration of 8 Quad Cables close packed on the diamond grid is illustrated in Figure 9.

Figure 9 • The placement of 8 Quad Cables (LEFT)

Figure 10 • Actual Quad Cables used in a Binder (RIGHT)

The coordinates of these 8 cables- corresponding to coordinates of their center points- are given by: Q-1 (1,1), Q-2 (2,2), Q-3 (3,1), Q-4 (1, 3), Q-5 (4,2), Q-6 (3,3), Q-7 (2,4), Q-8 (5,3)

The justification for this assumption is the observation of actual cable types used. Figure 10 shows photographs (obtained from a collection of photos on the Internet) actual Quad Cable Binders used for telephone loops. As indicated they are all “pressed together”- thus a close packed assumption can be justified. Placing each on the lattice point of a rectangular grid is a reasonable simplification that allows for analysis. **Assumption #2**-the geometric arrangement remains the same over the entire length of the cable- or at least over the length of a segment for which the full transmission line behavior is being considered. This assumption is justified by the observation that any action that does not compromise the continuity of a cable pair should not affect the topological closeness from one end the other. In other words, a twisting of the entire Binder should not affect the closeness.** Assumption #3**- While initially all Quads are close packed as time proceeds 3 principal causes will allow the distance between the Quads to increase. These causes are thermal transients- heating and cooling- naturally occurring mechanical vibrations- due to wind, rain and other weather effects- and mechanical vibrations due to vehicular traffic, construction and handling by technicians and others. Essentially, it is assumed that there will be a dilation of the close packing. There will be a slackening of the close packed configuration. This is very reminiscent of effects related to the Second Law of Thermodynamics. In a way, it may be related to the statistical approach used in [3]. However, further discussion of this is beyond the present contribution. Furthermore, this assumed dilations allow the results of the model to be applied to situations where the close packing is not rigidly carried out on a diamond grid but is limited by other physical constraints- for example requiring the individual Quads to be placed on the circumferences of concentric circles- thus increasing average distance between some.

Given these 3 Assumptions the following general points are made: FEXT is caused by capacitive imbalance between 2 pairs. When the pairs are in the same Quad this is termed “Intra- Quad FEXT.” When the pairs are in different Quads this is termed “Inter-Quad FEXT.” This capacitive imbalance itself is driven by the actual value of the capacitances between the individual wires. If this, did not exist then there would be no imbalance and no FEXT. The capacitance is expected to be maximum when the pairs are as close as possible -as in the same Quad- “Intra-Quad FEXT.” For “Inter-Quad FEXT” it is reasonable to assume that the capacitance is maximum when the corresponding pairs are adjacent on the Grid shown in the above Figure 7. This corresponds to a Euclidean Distance in Figure 7 = 1. The capacitance decreases between 2 cable pairs with the Euclidean Distance. However, the capacitance also decreases between 2 cable pairs if the area through which the Electric Flux protrudes is reduced. This may be caused by blockage if other cable pairs are between the 2 cable pairs of interest. If 2 cable pairs are adjacent, then there is no blockage. On the other hand, if 2 cable pairs are at the opposite far vertices of the square Grid shown in the above Figures then there is maximum blockage.

Let “C_{adj}” be the capacitance between 2 pairs which are in different Quads, but which are adjacent. Let “C” be the capacitance between 2 cable pairs of interest but each in a different Quad. Then:

C = ( 1 + χ) -1 [Cadj ]/ Euclidean Distance(25)

The division by Euclidean Distance corresponding to the reduced capacitance by separation. The first factor on the right side of (25) corresponds to the “blockage.” The term “χ” will = 1 if the 2 cable pairs are adjacent and there is no blockage. This is somewhat arbitrary- another value can be chosen. But, it is not unreasonable. Otherwise χ will increase with Euclidean Distance. For purposes of this present model it is not unreasonable to have:

χ = Euclidean Distance(26)

Proceeding on this basis, ignoring the “1” above and substituting (16) brings:

C = [C_{adj} ]/ [Euclidean Distance]^{2}(27)

and C/[C_{adj} ] = 1/[Euclidean Distance]^{2}

This is “almost” the “Amplitude Offset “factor, “θij.“ What is needed is to account for the “distance dilation” associated with Assumption 3. This is done through the factor “KD” – taken to be a positive number and

θij = 1/( K_{D} [Euclidean Distance between “’i” and “j”] )^{2} (28)

K_{D} is taken = 2. This “dilates” the Euclidean distance. Basically, we are assuming that each of the components causing the dilation- mentioned in Assumption #3- provides a dilation with the sum totaling to “2.” While this is an assumed value it is also a reasonable value. Because of mechanical constraints- such as the shield and any jacketing- the dilation must be limited-where “Euclidean Distance” refers to the “Euclidean Distance” between the separate Quads corresponding to loops “i” and “j” on the grid of Figure 6. When expressed in dB this is:

[θij ] dB = -40 Log[Euclidean Distance between “’i” and “j”] -12(29)

When considering a configuration of Quad Cables in a Binder- they are considered as “close packed”- with each Quad covering an empty “diamond” shape within the grid. For purposes of this model when determining the actual placement of the Quad Cables on the grid shown in Figure 6 - this should be done in the following way: Place the first Quad at the lattice point given by the coordinates (1, 1). For each additional Quad- place it at that currently empty lattice point with coordinates so that the Euclidean distance between it and (1, 1) is at a minimum. The empty lattice point must allow the placement of a Quad so that it is fully within the lattice. By way of example, the coordinate (2, 2) would be allowed but not (0, 3). The empty lattice point must be such that the Quad which has it as its center does not overlap any other Quad. By way of example the coordinate (2, 2) would be allowed but not (1, 2). This should always be done in this manner to allow consistency when computations are carried out.

For the example of the close packed 8 Quad Cables shown in Figure 8 it is interesting to compute the range of the Amplitude Offset. Note: this corresponds to 16 pairs with 2 pairs per Quad Cable. The greatest offset would be between cables Q-1 and Q-8. The Euclidean Distance here would be 20 ^{0.5} or 4.47. This corresponds to an Amplitude Offset of 26 dB. This is in the same range of values as obtained with the ATIS model [3] though a little less. But, this is to be expected. We are dealing here with 8 Quads- 16 cable pairs not the 25 cable pairs of the ATIS Model Binder. This also is representative of the measured data provided in [5]. Using the procedure described above an example Amplitude Offset Matrix [θij] dB corresponding to 4 Quad Cables- 8 pairs- is shown in Table 2 where each row/column number corresponds to a Pair number. These 8 pairs are identified by being in the following Quads: Quad 1: Pairs 1 and 2, Quad 2: Pairs 3 and 4, Quad 3: Pairs 5 and 6, Quad 4: Pairs 7 and 8, Quad 8: Pairs 15 and 16. The ‘0” entries in the matrix indicate that there is no Amplitude Offset between a Pair and itself and a Pair and its “partner” in the same Quad.

Table 2 • Example [θij] dB for 4 Quad Cables- 8 Pairs

It is worthwhile to compare the values in Table 2 with comparable values obtained by the statistical approach used in [3]. The upper left 5 x5 submatrix of the Amplitude Offset Matrix in [3] is provided in Table 5- though this corresponded to Unshielded Twisted Pair cables not Quad Cables. This Amplitude Offset Matrix in [3] is essentially “slightly asymmetric”- though there is a procedure for converting it to a symmetric matrix. Nonetheless, it is best to consider the “slightly asymmetric” version. Comparing the matrices in Table 2 and Table 3 it is evident that the values are in the same general range-though with those of Table 5 trending higher than those of Table 2. This provides credibility that both approaches are coming up with reasonable- though not identical- results given limits to the essential knowledge of the problem.

Table 3 • Submatrix of [θij] dB for twisted pair cables in [3]

It is also worthwhile noting that the average Amplitude Offset in Table 4 is -23.5417 dB.

**“Ψik “**

Using the approximation for Φik (f, X) given in degrees- this can be converted to radians by multiplying by 2 π/360 to obtain ΦRik (f, X). From this is obtained Ψik = βd + ΦRik (f, X) , where β is approximated by (Group Delay)f with “Group Delay” given a constant in (5).

**3. MODEL COMPARISON WITH EXPERIMENTAL MEASUREMENTS**

In concluding, a brief comparison is made of the predictions of the theoretical model to experimental measurements made of an actual PE4D-ALT used by Swisscom [12]. In the interest of conciseness attention will only be directed at the dependence of |ELFEXT| dB on frequency. Comparisons with respect the dependence of |ELFEXT| on exposure length, with respect to the phase of ELFEXT, direct path attenuation and Group Delay, and the Amplitude Offset are of interest but will not be dealt with. Figure 11 shows an intra-quad ELFEXT measurement of a of PE4D-ALT cable of 66m length consisting of 10 quads with wire diameter of 0.6mm. The measurement is compared with the ELFEXT calculation based on the parameter values assumed in this paper. Calculated and measured curves show a great similarity in shape but are not completely aligned e.g. the dips do not coincide exactly. This can be explained by the fact that the model parameter used were not fitted with the measurements. This would have to be done in a next step to get optimized parameter values. In addition, Figure 11 shows also the four-segment model developed in this paper, which was explicitly fitted to the measurement data shown in the same figure.

Figure 11 • Swisscom intra-quad |ELFEXT| measurement of PE4D-ALT 10x4x0.6mm cable of 66m length vs. calculation and model.

**Acknowledgements**

Mr. Marcel Reitmann of Swisscom was very helpful in providing experimental measurements for validating the analytical model. Mr. Seth Stowell and Dr. Knut Kongelbeck assisted with carrying out difficult computational experiments. Interaction with Professor (Emeritus) Dante Youla (PINY- New York University) was of great value. He provided the theoretical foundation for this modelling effort and invaluable insight into the many issues arising as it was carried out. Professor (Emeritus) John Murray (SUNY-Stonybrook) aided in the expansion of this theoretical foundation. The text and illustration editing provided by Mrs. Victoria Twomey was invaluable.

**References**

1. Youla, D.C., “Theory and Synthesis of Linear Time-Invariant Networks” Ch.14, Cambridge University Press, 2015.

2. Brillouin, L., “Wave Propagation in Periodic Structures,” McGraw-Hill, 1946.

3. “Mutliple-Input Mutliple-Output Crosstalk Channel Model,” ATIS-0600024, 4.2.1.1.

4. van den Brink, R,” Modeling the Dual-Slope Behavior of in Quad EL-FEXT in twisted Pair Quad Cables,” IEEE Transactions on Communications, Vol.65, No.5, May 2017.

5. Blenk, T., Stolle, R. and Strobel, R., “Analysis of Transmission Line Models for xDSL Systems, “ARC 2013.

6. Strobel, R., Stolle, R., Utschick, W., “Wideband Modeling of Twisted Pair Cables for MIMO Applications,” Global Communications Conference (GLOBECOM), 2013.

7. Broadband Forum Technical Report, TR-285 “Broadband Cable Models,” Issue 1, February 2015.

8. Campbell, G. A., “Crosstalk Formulae for Non-Loaded Circuits,” Bell System Technical Journal, vol.14, no. 4, 1935, P 528.

9. Granzow, Kenneth D., “Digital Transmission Lines- Computer Modelling and Analysis,” P 68, Eq. 5-39, Oxford University Press, 1998.

10. Freeman, Jon C., “Fundamentals of Microwave Transmission Lines,” P140, Eq. 3-36, John Wiley and Sons, 1996.

11. Mnaouer, Kachout; Hadj, Bel; Jamel, Tahar; Fethi, Choubani; “Crosstalk Prediction for Three Conductors Nonuniform Transmission Lines: Theoretical Approach & Numerical Simulation”- Kachout Mnaouer, Bel Hadj Tahar Jamel, Choubani Fethi, Journal of Electromagnetic Analysis and Applications, Vol. 3 No. 8 (2011)

12. Swisscom Expérimental Measurements.

13. TR-285 “Broadband Copper Cable Models,” Table 3., Issue 1 Amendment 1, March 2017.

**About the Author**

Kenneth S. Schneider is the CEO and founder of Telebyte, Inc., which is focused on the development, manufacture and marketing of test equipment for the broadband telecommunications market. He received the BS, M. Eng. (Elect) and PhD degrees all from Cornell University. Dr. Schneider has been active in the development of communications technology throughout his career. This included work as a member of technical staff at Hughes Aircraft Company, M.I.T. Lincoln Laboratory, and Network Analysis Corporation.. He has also taught communication theory at the Polytechnic Institute of New York. He has published more than 100 technical papers, holds three patents, and is the recipient of the IEEE (Long Island Section) Harold Wheeler award.

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