Tape Recording and Reproducing Frequency Response

Jay McKnight

Here is the info on the magnetic tape recording and reproducing calculation based on Neal Bertram's papers that I sent you.

I also attach my turnkey Forth program for calculating response. This runs on a PC under DOS.  This calculation assumes a lossless recording and reproducing system, biased for maximum senstitivity at long wavelength, with the magnetic properties as listed below:

The dates are only approximate. Listed by approximate date of introduction, oldest to newest (I think).

Reversible Permeability of Magnetic Tapes 

Peng Luo, UC San Diego Center for Magnetic Recording Research (CMRR)
Tape Manufacturer & Type Coating Thickness/
mu sub x mu sub y alpha beta
Genoton homogeneous (1950s) 55 1.40 1.38 1.02 1.39
3M 111 (1948...1960s) 11.2 3.02 3.49 0.93 3.25
2M 206 (1970s)(The IEC "Reference Tape") 13.7 2.01 2.42 0.91 2.21
Ampex 462 (Consumer / duplicator tape) 10.7 1.73 2.68 0.66 2.15
Ampex 406 12.7 1.75 1.99 0.94 1.87
Ampex 456 14.0 1.56 3.67 0.65 2.39
Ampex 499 16.5 1.47 2.84 0.72 2.04
Ampex 705 (Slow-speed Logging tape)) 4.3 1.77 3.26 0.74 2.40
BASF SM911 16.0 1.93 3.18 0.78 2.48

I have the blank tapes that Peng measured, and I want to some day measure the frequency responses, and compare with the values calculated from these parameters.

I have checked the results of the Forth program response calculations against Fig 3 of Neal's paper, and they seem to agree (as well as one can tell against a coarse-scale graph). Note that Neal's calculation is an "absolute response", and the maxumum sensitivity is 1/2 (level -6 dB), which I have normalized out of my calcusations.

I also attach the source program for this Forth application. Forth is reverse-Polish-notation (parameters on stack before executing operations); one defines a set of "words" (which are in effect subroutines) in terms of previously-defined words; then the final definition is "the program".  Backslash marks a comment. Curly brackets {} delimit the lines that are executed. This program uses a software floating point, so does not require a floating-point chip.