Nonlinearly variable gain apparatus
STATEMENT OF GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon. 
    
    
     BACKGROUND OF THE INVENTION 
     There are many uses for an apparatus which can produce an inverted logarithmic S curve of gain versus potentiometer rotation while using a linear resistance taper potentiometer. Prior art did not produce this curve and used only passive components such as T-pads with special taper characteristics. Disadvantages of the prior art include cost of special taper components, amplitude loss rather than gain, and strict termination impedance requirements. Advantages of the invention over the prior art include active gain, selectable impedance for input and output without affecting performance and most importantly, the use of a standard linear taper potentiometer. 
     SUMMARY OF THE INVENTION 
     A nonlinearly variable gain apparatus is provided. An operational feedback circuit uses a linear potentiometer and a resistance network to produce an inverted logarithmic S curve of gain versus potentiometer rotation. The circuit is useful where a very accurate gain setting is required above a normal point but greater variation is required away from this point. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     A single FIGURE shows partly in block and partly in schematic form the preferred embodiment. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Now referring in detail to the preferred embodiment, three is shown equation 1 which is: ##EQU1## Equation 1 is taken in conjunction with the single figure and gives a voltage gain expression. In the equation the potentiometer resistance has been expressed as two resistances from the wiper tap to the two ends of the resistance element. 
     In the single figure, there is shown voltage in (Vi) at point 10 and voltage out (Vo) at point 20. Amplifier 19 receives V+ and V- voltage. At the positive input thereof there is shown resistor 18 (R8) connected to ground. From the output of amplifier 19, resistor 12 (R2) is connected in series with resistor 13 (R3) to ground. Linear potentiometer 21 is connected from the output of amplifier 19 to ground. Linear potentiometer 21 is shown as being comprised of resistors 14 (R4) and 15 (R5). Resistor 16 (R6) is connected from point 22 to the negative input of amplifier 19. The negative input of amplifier 19 is also connected to ground by way of resistor 17 (R7). 
     In the operation of the nonlinearly variable gain circuit, resistor 14 (R4) varies linearly from R max  to zero with clockwise rotation and resistance 15 (R5) varies linearly from zero to R max  at the same time. Total resistance remains constant as R4+R5=R max , the total potentiometer resistance. Circuit gain at the center of rotation is set by resistors 12 (R2) and 13 (R3), while eccentricity is set by resistor 11 (R1). A total scale factor is introduced at all rotations by resistors 16 (R6) and 17 (R7). Circuit gain is positive (noninverting) and must lie in the region from +1 to +∞. Maximum gain is practically limited to some finite value depending upon the desired bandwidth and choice of operational amplifier. 
     Use of the circuit is indicated where normal operation requires a very accurate gain setting about some nominal point but abnormal operation requires less accurate gain settings farther from the nominal point. Expressed as a derivative this means that the slope of the gain versus rotation curve (db/degree) should be small near the nominal point and become larger as gain is varied from the nominal point. 
     Alternate embodiments of the invention may use transistors instead of operational amplifier gain, or may use a different taper potentiometer to obtain modified inverted S curves.