GB1356113A - Charge-time responses of dielectrics - Google Patents

Abstract

1356113 Digital calculating apparatus; analogue-to-digital converter IMPERIAL CHEMICAL INDUSTRIES Ltd 11 May 1970 [29 May 1970] 25945/70 Addition to 1292332 Headings G4A and G4H [Also in Division G1] The complex permittivity e*(#) of a dielectric is obtained by calculating the Fourier transform of the current i(t) that flows as a result of applying a known potential across the dielectric. Thus and where q(t) is the charge on the dielectric and is the variable that is actually available in the form of an amplitude significant voltage for use in the calculation. The integral is evaluated, approximately, by dividing the range into a set of contiguous intervals where #t 1 = 1 and n = 2<SP>p</SP>,p = 0, Œ1, Œ2 ..., Œ#, and by assuming that within each such interval q(t) varies linearly with log t. Thus, within the above interval it is assumed that From which, by differentiation, it follows that where #q(n) = q(#2nt 1 )-q(#2nt 1 ). This value of i(t) is now substituted into the original integral, giving from which the real and imaginary components, denoted by e<SP>1</SP>(#) and e<SP>11</SP>(#) respectively, may be extracted in the form and where and since #t 1 = 1. I.e., x(n) and y(n) are constants which can be tabulated. The y coefficients have a maximum of y(1) = 0À83, when p = 0, and diminish numerically as |p| increases. For example when p = Œ5, y(32) = -0À06 and y(1/32) = 0À03. Noting this fact, and by way of a further approximation, only a few values of #q(n) centred around n = 1 are used in evaluating the above series (2) for e<SP>11</SP>(#). For example, using five values of #q(n), the following approxi mation can be used - The Specification also mentions that 3 term (i.e., using three values of #q(n)) and 1 term approximations may be used. A similar approximation for e<SP>1</SP>(#) may be derived but since the values of the x coefficients are all substantially unity when p is negative, for example x(¢) = 0À86, x(“) = 0À96, x(#) = 0À99, the term corresponding to y 0 (“)#q(“) in the approximation above for e<SP>1</SP> is modified. The five term approximation for e<SP>11</SP> used by the Specification is where The additional term q(¢#2/4t 1 ) requires no additional measuring since it is required in computing #q(“). Thus, this method shows how to evaluate e*(#) approximately, for a particular value # 1 of #, and in particular, using the five term approximations, it requires that the values of q(t) be known at the instants of time #2t 1 , “#2t 1 , ¢#2t 1 , #2t 1 , 2#2t 1 and 4#2t 1 , where # 1 t 1 = 1. To obtain an approximation to the function e*(#), the method has to be applied repeatedly for different values of #, so that a graph can be drawn. A block diagram (Fig. 13, not shown) of a suitable data processing arrangement is described. A voltage sampling and digitizing arrangement, Fig. 9, is also described in which the voltage v(t) to be digitized is applied via a normally closed F.E.T. switch S1 to a capacitor C1 and when a sample is required switch S1 is opened and about 1ms. later a switch S2 is opened- 1 ms being sufficient for capacitor C2 to charge to the level of C1. The sample value of v(t), which is now on capacitor C2, is digitized by discharging the capacitor linearly via a resistor R2 towards -V, and counting clock pulses 92 until the potential on capacitor C2 reaches zero.