6- 5.1 Usage

Experimental data from transfer-function tests consist of records of signals from which transfer functions or related quantities are to be extracted. Tables 6.10 and 6.11 indicate that there are a variety of approaches to data acquisition and analysis This section treats those which operate on the signals in the time domain to obtain a transfer function Section 6-6, Frequency Analyzers, is devoted to analysis in the frequency domain.

The signals to be analyzed can consist of any or all of the following components a single frequency, a continuum
of frequencies having meaning to the test, and unwanted frequencies, either discrete or continuous. In general, the purpose of an analyzer is to separate these three with the primary purpose of picking out the first two in the presence of the third.

Results from time-domain analyzers can be expressed ultimately in the frequency domain. For tests where a single frequency is excited, the combined results from a number of sequential tests at various frequencies constitute a transfer function evaluated at those frequencies If a continuous frequency is used m external excitation or self-excitation, the correlation function obtained in the time domain may be subsequently Fourier analyzed, as indicated in Table 6.1, to obtain the desired frequency function.

6- 5.2 Null-Balance Analyzer

The principle behind the null-balance method of analyz­ing sinusoidal excitation experiments is one of nulling or bucking out the output signal with the input signal. Here the transfer function is simply the gain and phase adjust­ment used on one signal or the other to achieve this cancellation. A number of rod-oscillator tests have used this method successfully.1 4 л s’2 6 However, the method is not applicable to analysis of a continuum of frequencies, as in pseudorandom excitation

Figure 6.12 shows schematically how the oscillating component of the ion-chamber current, Ij sin(cot + 6), is nulled against a mechanical oscillating signal to a sine potentiometer from the excitation device By having a sinusoidal resistance variation m the potentiometer through which the ion-chamber current flows, you obtain a mixed
signal whose sin cot components are nulled by resistance and mechanical phase adjustments Usually the output (Fig 6 12) is sent through a band-pass filter (for fre­quencies near that of the oscillator and observed by an operator making the nulling adjustments Some skill is required for high precision.

6- 5.3 Synchronous Transfer-Function Analyzer

A specially constructed analyzer has been used in rod-oscillator experiments11,15 and has been found to give high-precision results The basic principle, as indicated in Fig. 6 13, is to multiply the ion-chamber signal (with its steady-state component bucked out) by sin cot or cos cot using a synchro-resolver whose mechanical input signal is precisely in phase with the rod-oscillator device Since

I] sin (cot + 0) = Ii sin cot cos в + Ii cos cot sin в (6 32)

integration of sin cot or cos cot times the right-hand side of

Eq 6 32 over an integral number of cycles gives a result proportional to Ij cos 0 or It sin0, respectively. The amplitude and phase of the ion-chamber current may then be obtained from these two integrated outputs

Amplitude = [(Ij cos0)2 + (Ij sin 0)2 і’"4 (6 33)

Tangent of phase = — 1 Sm ^ (6 34)

11 cos 8

As indicated in Fig. 6.13, the signal at the point of the modulator modulates a carrier (typically several hundred Hertz), which is later demodulated at the demodulator

Regarding the noise accompanying the signal I] sin(cot + 0), the analyzer acts as a sharply tuned filter at со. The noise near со will cause randomness in successive determinations of Ii and в, the randomness being proportional to the noise and inversely proportional to the integration time