. Electronic apparatus for biological research . o) —^ Figure degree of damping depended on the relative sizes of 1/LCand R^jAL^, which is the same as depending on the sizes of 1/C and R^I4L. It thus appears that Q and the degree of damping are closely related, and in particular that at critical damping Q = ^; series resonant circuits are below critical damping if Q > ^, and more than critically damped if Q < |. We can now consider the relevance of Graphs 21 and 22 to the electro- magnetic penwriter. The input current flows through a coil to produce a force F on a moving mechanical s
. Electronic apparatus for biological research . o) —^ Figure degree of damping depended on the relative sizes of 1/LCand R^jAL^, which is the same as depending on the sizes of 1/C and R^I4L. It thus appears that Q and the degree of damping are closely related, and in particular that at critical damping Q = ^; series resonant circuits are below critical damping if Q > ^, and more than critically damped if Q < |. We can now consider the relevance of Graphs 21 and 22 to the electro- magnetic penwriter. The input current flows through a coil to produce a force F on a moving mechanical system of mass M constrained by a spring of stiffness X and viscous damping d. If the displacement produced is s, then we have . d5 , d^j' and the actual force available for displacing the pen is Fpen = Xs, the remain- der of F being used in overcoming the inertia and viscous damping forces. Comparing this with dq q d^q ^ = ^d7 + c + ^d^ where the capacitance voltage is v^ = qjC, we see that the pen deflection is analogous to capacitance voltage. Hence, if a current be suddenly applied to a penwriter, the pen movement has one of the forms of Graph 21, depend- ing on the amount of viscous damping present. If an alternating current of constant amplitude and variable frequency be fed to a penwriter the device records, without distortion, up to a certain frequency, where there is a greater or lesser resonance, depending upon the amount of damping, and above this frequency the performance of the device falls off rapidly. From Graph 22 it appears that a Q value of rather less than one will give the pen- writer an optimum distortion-free band-width. Impedance of series resonant circuit The impedance of a series resonant circuit at frequencies away from reso- nance is important in the design of certain tuned amphfiers. 76
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