THE CORRELATOGRAPH 1179 



inputs applied across the two diagonals and the output taken off one 

 pair of input terminals through a low pass filter. Each varistor is operated 

 in a substantially square law range. If A and B represent the two inputs, 

 we try in effect to produce an output proportional to 



{A + Bf - (A - Bf = ^AB. 



The necessary conditions are conveniently expressed in terms of sine 

 wave inputs in order that analyzer measurements may be used as a check 

 on accuracy. Let P cos pt represent a typical component of the signal 

 impressed as one input to the multiplier and Q cos qi a typical component 

 simultaneously applied to the other input terminal. The product is 



PQ pQ 



{P cos pi)iQ cos qt) = -^ cos ip -\- q)t -]- -^ cos {p — q)t. 



Since our purpose is to integrate the output of the multiplier over a time 

 interval relatively long compared to the periods of components within 

 the signal band, we have no interest in the product component of fre- 

 quency p •\- q and in fact filter out such components immediately along 

 with the original signal components to prevent loading the product 

 amplifier with unessential waves. A significant test on the accuracy of 

 the multiplier is therefore the fidelity with which the amplitude of the 

 difference frequency term cos {p — q)t follows the product of the ampli- 

 tudes of cos pi and cos qt. This is not sufficient in itself however because 

 it does not give a check on the balancing out of the squares of the in- 

 dividual inputs. To test the latter we superimpose the two components 

 P cos pi and Q cos qt on one input circuit with no signal applied to the 

 other input and measure the output component of frequency p — q. 

 We also repeat the measurement with the two sine waves impressed on 

 the second input and nothing on the first input. Typical results are shown 

 in Fig. 5. The varistors were selected by R. R. Blair from persistent 

 screen cathode ray tube displays of the characteristics. The square law 

 region is enlarged and the output increased by applying a direct current 

 bias to the bridge through a series resistance. This form of multiplier 

 copies a design worked out by R. R. Riesz for a different purpose. 



The product output of the multiplier is weak at best because a rela- 

 tively small range of varistor inputs fit the necessary law. A fairly high 

 gain product amplifier is therefore provided. Fortunately we do not have 

 to amplify a band which extends all the way down to zero frequency. The 

 significant component when calculating the autocorrelation function of P 

 cos p^ for lag time r is (PV2) cos pr, which is constant only when p = 

 or r is constant. Our lowest value of p corresponds to 1600 cps. The value 



