Abstract
An efficient frequency-based clock analysis method: CSAV is proposed in this paper. It computes the circuit response by first solving the state equation in frequency domain, and derive the rational approximate with the help of vector fitting [9]. There are two aspects that contribute to the time efficiency of the method. One is CSAV solves the state equation only on selected frequency points, which significantly reduce the amount of time for equation solving. The other is CSAV performs vector fitting and waveform recovery only on user specified nodes, which save the unnecessary computation on the nodes which are not concerned by user. The complexity of our method is O( lceillg f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> rceilN <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sup> + lceillg f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> rceil <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out</sub> ), where f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> is proportional to the knee frequencyquency of input signal, N is the node number of the circuit, a is a constant around 1.3, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> is the order of approximation and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out</sub> is the number of output nodes. Our experimental results show that compared with Hspice, CSAV achieves speed-up up to 35 times while the error is only 1%. Moreover, computational saving of CSAV grows with circuit size, which makes this method especially promising for large cases.
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