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US 7,584,238 B2Granted
Analog circuit system for generating elliptic functions
AssigneeDeutsche Telekom AG
InventorKlaus Huber
Life of this patent
Estimating the term…
Abstract
An analog circuit system for generating output signals whose curve shape, at least sectionally, corresponds or is approximate to an elliptic function. Standard analog components such as adders, integrators, multipliers and differential amplifiers can be interconnected in order to simulate elliptic time functions from the standpoint of circuit engineering.
Claims7
An analog circuit system, comprising:
- a plurality of analog multipliers;
- a plurality of analog integrators;
- and
- a plurality of analog computing circuits, each analog computing circuit having at least one analog multiplier of the plurality of analog multipliers and analog integrator of the plurality of analog integrators,
- wherein the plurality of analog multipliers and the plurality of analog integrators are interconnected so that the analog circuit system delivers three output signals whose curve shapes, at least sectionally, respectively correspond to the Jacobi elliptic time functions
- sn
-
- (
- 2
-
-
- π
- ^
- T
- ·
- t
- ,
- k
- )
- ,
- cn
-
- (
- 2
-
-
- π
- ^
- T
- ·
- t
- ,
- k
- )
-
-
- and
-
-
- dn
-
- (
- 2
-
-
- π
- ^
- T
- ·
- t
- ,
- k
- )
- ,
- where
-
-
- π
- ^
- =
- π
- M
-
- (
- 1
- ,
- 1
- -
- k
- 2
- )
- and M(1, √{square root over (1−k2)}) represents the arithmetic-geometric mean of 1 and √{square root over (1−k2)}, and k lies in the interval [0, 1].
69 more elements
An analog circuit system comprising:
- an analog computing circuit for calculating a minimum from two input signals;
- an analog computing circuit for calculating a maximum from two input signals;
- an analog computing circuit for calculating an arithmetic mean from two input signals;
- an analog computing circuit for calculating a geometric mean from two input signals,
- wherein an output of the analog computing circuit for calculating the minimum is connected to the input of the analog computing circuit for calculating the arithmetic mean and the input of the analog computing circuit for calculating the geometric mean,
- wherein an output of the analog computing circuit for calculating the maximum is connected to another input of the analog computing circuit for calculating the arithmetic mean and another input of the analog computing circuit for calculating the geometric mean, the input of the analog computing circuit for calculating the minimum is connected to an output of the analog computing circuit for calculating the arithmetic mean, and a factor 1 is applied to the other input, and
- wherein the input of the analog computing circuit for calculating the maximum is connected to an output of the analog computing circuit for calculating the geometric mean, and a factor (1−k2) is applied to the other input, so that an arithmetic-geometric mean M(1, √{square root over (1−k2)}) is present at the output of the analog computing circuit for calculating the geometric mean and at the output of the analog computing circuit for calculating the arithmetic mean.
4 more elements
An analog circuit system comprising:
- a plurality of analog computing circuits which generate at least one output signal whose curve shape, at least sectionally, corresponds to an elliptic function,
- a first multiplier, at whose inputs the input signal of the variable x and a factor (1−k2)/2 are applied,
- a second multiplier, at whose inputs a triangular input signal and a factor (1+k2)/2 are applied,
- a differential amplifier that, on the incoming side, is connected to ground and to the output of the second multiplier, and
- an adder that is connected to the output of the first multiplier and the output of the differential amplifier, an output signal that is combined with the input variable x by the Jacobi elliptic function sn(x, k) being present at the output of the adder,
- wherein the plurality of analog computing circuits are interconnected in such a way that, with an input signal of the variable x, the output signal of the circuit system approximatively delivers the value sn(x, k).
3 more elements
Dependencies are inferred from the claim text.