The Biased Ideal Rectifier 



By W. R. BENNETT 



Methods of solution and specific results are given for the spectrum of the 

 response of devices which have sharply defined transitions between conducting 

 and non-conducting regions in their characteristics. The input wave consists 

 of one or more sinusoidal components and the operating point is adjusted by bias, 

 which may either be independently applied or produced bv the rectified output 

 itself. 



Introduction 



THE concept of an ideal rectifier gives a useful approximation for the 

 analysis of many kinds of communication circuits. An ideal rectifier 

 conducts in only one direction, and by use of a suitable bias may have the 

 critical value of input separating non-conduction from, conduction shifted 

 to any arbitrary value, as illustrated in Fig. 1. A curve similar to Fig. 1 

 might represent for example the current versus voltage relation of a biased 

 diode. By superposing appropriate rectifying and linear characteristics 

 with different conducting directions and values of bias, we may approximate 

 the characteristic of an ideal limiter. Fig. 2, which gives constant response 

 when the input voltage falls outside a given range. Such a curve might 

 approximate the relationship between flux and magnetizing force in certain 

 ferromagnetic materials, or the output current versus Signal voltage in a 

 negative-feedback amplifier. The abrupt transitions from non-conducting 

 to conducting regions shown are not realizable in physical circuits, but the 

 actual characteristics obtained in many devices are much sharper than can 

 be represented adequately by a small number of terms in a power series 

 or in fact by any very simple analytic function expressible in a reasonably 

 small number of terms valid for both the non-conducting and conducting 

 regions. 



In the typical communication problem the input is a signal which may 

 be expressed in terms of one or more sinusoidal components. The output 

 of the rectifier consists of modified segments of the original resultant of the 

 individual components separated by regions in which the wave is zero or 

 constant. We are not so much interested in the actual wave form of these 

 chopped-up portions, which would be very easy to compute, as in the fre- 

 quency spectrum. The reason for this is that the rectifier or limiter is 

 usually followed by a frequency-selective circuit, which delivers a smoothly 

 varying function of time. Knowing the spectrum of the chopped input 

 to the selective network and the steady-state response as a function of 



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