this invention pertains to a solid - state capacitor multiplier which could be used in any application where a large coupling or decoupling capacitor is required . some of the most common applications could include power supplies , low frequency signal amplifiers , audio amplifiers , power amplifiers , telephone voice frequency repeaters . the invention as depicted in fig4 shows a coupling / decoupling capacitor multiplier 10 of the invention which is connected to an ac voltage source 12 and a load rl . the multiplier 10 includes an amplifier means such as op - amp a1 having a non - inverting input connected to the ac voltage source 12 . a capacitor c1 is connected to the output of op - amp a1 and to a load output 14 of the capacitor multiplier 10 . a capacitor c2 is connected to inverting input of the op - amp a1 and to the load output 14 of the capacitor multiplier 10 . a resistor r is connected between the inverting input of op - amp a1 and the output of op - amp a1 . r is in series with c1 and c2 . the c2 and r junction is connected to the inverting input of the op - amp a1 , and the c1 and r junction is connected to the output of op - amp a1 . resistor rs1 in series with c1 , and resistor rs2 in series with c2 , are equivalent series resistance for the respective capacitors . c1 and c2 are connected at the load output 14 of the multiplier 10 . the dc voltage at the load output 14 is independent of the operating voltage characteristics of the op - amp 14 as the op - amp does not see the dc voltage at load output 14 . the multiplier 10 is shown in a floating embodiment and to achieve grounded decoupling , the non - inverting input of op - amp a1 is connected to ground at 16 as shown in fig4 . to understand the invention , equations pertaining to the operation of the circuit will be developed for ceq ( equivalent capacitance of the multiplier 10 ) and req ( equivalent series resistance of the multiplier 10 ). while the equations are derived for the grounded application , the ultimate result will be the same for the floating capacitor application . the equations for ceq and req will now be developed for the following three sets of conditions where : in the first set of conditions , where capacitor c1 and c2 are lossless , that is , rs1 and rs2 equal zero , assume further that v2 is much greater than vc2 , v1 , and v -- , and further assume that input impedance of an op - amp equals infinity , we may then state the following equation , ## equ2 ## where k ( s ) is the open loop gain of the op - amp a1 . then the following equations express the value of ceq and req : ## equ3 ## for 1 / sc2 & lt ;& lt ; r ## equ4 ## consequently , ## equ5 ## in conclusion , with lossless capacitors c1 and c2 , the circuit of fig4 shows that the equivalent capacitor ceq is equal to the product of c1 and the open loop gain of the op - amp a1 and req equal to the products of the impedance of c1 and c2 divided by resistor r . thus , if the values of ceq and req are preselected , then other circuit elements can be sized to get the desired result . for example , if ceq and the characteristics of the op - amp a1 are known , then c1 will be equal to the ceq divided by k ( s ), the gain of the op - amp a1 . for the second set of conditions where capacitor c1 is lossless and capacitor c2 is lossy , that is rs2 has value , then the following equations apply : ## equ6 ## for the third set of conditions where c2 is a lossless capacitor and c1 is a lossy capacitor , which is the most practical application the following equations express the values of ceq and req : ## equ7 ## with a lossy capacitor c1 and a lossless capacitor c2 , the result is ceq and req expressed by the above equations . since req of a typical electrolytic capacitor is typically in the range of a fraction of an ohm to a few ohms , resistor r could be a few megohms which would result in the ceq being close to the product of the open loop gain of the op - amp a1 and the capacitor c1 with the req also being decreased in value . in selecting the values of the circuit parameters , it should be noted that the entire load current passes through c1 . consequently , the voltage drop across c1 may be substantial but it cannot be greater than the maximum voltage swing that the op - amp a1 can deliver . ideally , c2 should be a lossless high quality capacitor having a value smaller than c1 . the size criteria selection for c2 is not as critical . the impedance of c2 may be smaller than r , and this is recommended because a large r is much more economical to obtain . while r may be large , there are limitations in practice as to its ultimate size . bias currents of op - amp a1 must be considered and , while r may be made large , it must not be larger than permissible in view of its compatibility with op - amp a1 . the op - amp a1 inherently has offset current , and the voltage at the non - inverting input of op - amp a1 would be the product of the bias current plus the offset current and resistor r . consequently , the voltage at the non - inverting input could become large with a large r , and if it exceeded the supply voltage , the op - amp a1 would not function . thus , r cannot exceed a range in value which would make it incompatible with the op - amp a1 . the equations expressing values for ceq and req for the three conditions described herein allow the determination of the values of r , c1 and c2 within the described limitations for r , c1 and c2 . for example , the desired values for ceq and req may be substituted in the equations and the values for r , c1 and c2 determined accordingly . the invention is not limited to the particular details of the circuit depicted and described , and other modifications of the application are contemplated . certain other changes may be made in the above described circuit without departing from the true spirit and scope of the invention herein described . it is intended , therefore , that the subject matter in the above depiction shall be interpreted as illustrative and not in a limiting sense .