Manhattan equation for the operational amplifier

Tunable high-Q resonator by general impedance converter

“…in order to increase Q-factor is necessary to use simultaneously high open loop gain G 0 = 1/α 0 and high crossover frequency f c . In some sense these results are derived by the Manhattan equation 16 in action.…”

“…In our example r 5 = r 3 = 1 kΩ, r 2 = r 1 = 100 Ω, and metallized polyester film capacitor C 4 = 10 µF, which gives L = 10 H. This set-up was given at the 7 Experimental Physics Olympiad. 14 If the GIC is sequentially connected to a load resistor r l , as presented in Fig. 2, the sequential impedance becomes Z s ≡ Z + r l .…”

“…( 14) deserves a detailed analysis. According to the Manhattan equation 16 for the openloop gain Eq. ( 2) G( f ) ≈ (1/G 0 + j f / f c ) −1 the crossover frequency 10 is defined as a frequency for which |G( f c )| = 1, that is why this frequency is also called unity gain frequency.…”

Simple do-it-yourself experimental set-up for electron charge qe measurement

“…giving the relation between the inputs U + and U − and the output U output of the OpAmp; for the numerical values of the parameters see Table II), precise measurement of the values of all components etc. The master equation of the OpAmps that apparently has never been published before (the authors will very much appreciate receiving an appropriate reference with the equation present in it) is described in our recent eprint [26] and the results of its application can be found in many technical applications. See for example the formulae for the frequency dependence of the inverting amplifier and non-inverting amplifiers in the specification of ADA4817.…”

Scientific instrument for creation of effective Cooper pair mass spectroscopy

“…8. For this study we re-derived the Manhattan equation of OpAmps [25], applied it in the theory of amplifiers [26], and studied statistical properties of the crossover frequency of the crossover frequency f 0 of the used low-noise OpAmp ADA4898-2 [27].…”