JP2004252711A - Circuit simulation method, device and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a circuit simulation method, device and program which will not force an operator of circuit simulations to reset relaxation values in implementing Gmin-Stepping method which is a solving method comprising performing solution determining processes while regarding pn junctions as diodes and inserting a virtual resistance Gmin having a virtual conductance in parallel with each diode, and, once a solution converges, performing an operation such as division or subtraction using the relaxation values to reduce the value of the virtual conductance, and performing the solution determining processes again. <P>SOLUTION: When a solution does not converge in solution determining processes (S303-S305) such as a Newton method and predetermined canceling requirements (S305: for example, whether or not the number of times that the Newton method is repeated exceeds an upper limit) are satisfied, the relaxation rate Grate1<SP>(k)</SP>of a relaxation value 10<SP>Grate</SP>is changed (S301) and the solution determining processes are performed again. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

【００２５】
ここで、Ｘは各ノードにおける電圧と各ブランチを流れる電流とをパラメータとして含む未知変数である。また、Ｒは未知変数Ｘの各パラメータが実数であることを、ｎはパラメータの個数をそれぞれ示している。また、Ｇｍｉｎは仮想抵抗Ｇｍｉｎにおける仮想コンダクタンスの値を示すパラメータである。
【００２６】
以下に、回路網方程式求解部２０における回路網方程式の作成および求解処理について述べる。なお、図３においては、各ステップにおける処理事項を示すとともに、Ｃ言語表記に基づいた命令式を［ ］中に併記している。
【００２７】
まず、Ｇｍｉｎ−Ｓｔｅｐｐｉｎｇ法における演算に用いる緩和値の変更回数を規定するカウンタｋの値を初期値１に設定する（ステップＳ３００）。なお、緩和値とは、仮想コンダクタンスを減少させる演算に用いられる値のことである。
【００２８】
次に、仮想コンダクタンスＧｍｉｎの緩和因子Ｇｒａｍｐを初期値Ｇｒａｍｐ０に設定する。なお、緩和因子Ｇｒａｍｐとは、１０^{Ｇｒａｍｐ}の形で仮想コンダクタンス基準値Ｇｍｉｎ０に乗算されることにより仮想コンダクタンスＧｍｉｎの値を緩和するパラメータのことである。
【００２９】
また、Ｇｍｉｎ−Ｓｔｅｐｐｉｎｇ処理一回当たりの緩和因子Ｇｒａｍｐの変更回数をカウントするカウンタｊの値を初期値１に設定する。さらに、仮想コンダクタンスＧｍｉｎの緩和割合Ｇｒａｔｅ１^（ｋ）を、緩和割合初期値Ｇｒａｔｅ０、カウンタｋおよび緩和割合減少率Ｇｒｉｎｃの各値を用いて設定する（以上、ステップＳ３０１）。なお、緩和割合Ｇｒａｔｅ１^（ｋ）は、具体的には図３に示すように、Ｇｒａｔｅ１^（ｋ）＝Ｇｒａｔｅ０＋（ｋ−１）×Ｇｒｉｎｃと設定される。
【００３０】
なお、Ｎｅｗｔｏｎ法では未知変数Ｘを順次、更新する。また、Ｇｍｉｎ−Ｓｔｅｐｐｉｎｇ法では仮想コンダクタンスＧｍｉｎの値を逓減させてゆく。よって、上記の式１は、カウンタｊと、Ｎｅｗｔｏｎ法の反復回数を規定するためのカウンタｉとを用いて下記の式２のように表される。
【００３１】
【数２】

【００３２】
そこで、仮想コンダクタンスＧｍｉｎ^（ｊ）を、仮想コンダクタンス基準値Ｇｍｉｎ０および緩和因子Ｇｒａｍｐの各値を用いて所定の初期値に設定する。そして、カウンタｉの値を初期値１に設定する。また、Ｎｅｗｔｏｎ法における回路網方程式の解（＝未知変数）Ｘを所定の初期値（例えば電圧Ｖ１，Ｖ２，…等）に設定する（以上、ステップＳ３０２）。なお、仮想コンダクタンスＧｍｉｎ^（ｊ）は、具体的には図３に示すように、Ｇｍｉｎ^（ｊ）＝Ｇｍｉｎ０×１０^{Ｇｒａｍｐ}と設定される。
【００３３】
さて、以上の設定を経て、Ｎｅｗｔｏｎ法により上記の式２の作成および求解処理を行う。Ｎｅｗｔｏｎ法では、未知変数Ｘを順次、更新して、下記の式３に基づく演算を行う。なお、式３は繰り返し回数（ｉ＋１）回目の解を示す。また、ステップＳ３０２に示したように、ｉ＝１の場合の解Ｘの初期値は回路シミュレーションのオペレーターが予め設定する。
【００３４】
【数３】

【００３５】
すなわち、第ｉ回目の未知変数Ｘの値に基づいて、順次、第ｉ＋１回目の未知変数Ｘの値を求めることにより、式２を満たす真の解に近づけてゆく求解処理が行われる。そして、求められた未知変数Ｘの変化量が予め指定された許容誤差の範囲内に収まれば、未知変数Ｘの解が収束して真値が得られたとみなし、計算を終了する。一方、指定の反復回数に達しても、未知変数Ｘの変化量が許容誤差の範囲内に収まらなければ、所定の打ち切り条件が満たされたとして未知変数Ｘの解が収束せず真値が得られなかったとみなし、計算を終了する。
【００３６】
Ｎｅｗｔｏｎ法による求解処理は上記のごとくであり、図３においてステップＳ３０３〜Ｓ３０５の各工程により実現される。すなわち、まず、回路情報のデータに基づいて式２の作成を行う。そして、式２の左辺中の未知変数Ｘ^（ｉ）に第ｉ回目の解（ｉ＝１の場合は初期値）を代入して式３中のＦ（Ｘ^（ｉ），Ｇｍｉｎ^（ｊ））を計算し、ヤコビアン∂Ｆ／∂Ｘをも計算することにより、第ｉ＋１回目の未知変数Ｘ^{（ｉ＋１）}を計算する（ステップＳ３０３）。
【００３７】
そして、得られた未知変数Ｘ^{（ｉ＋１）}と第ｉ回目の解Ｘ^（ｉ）との間の変化量を算出し、その差が回路シミュレーションのオペレーターによって予め設定された許容誤差の範囲内に収まっているかどうかにより、未知変数Ｘ^{（ｉ＋１）}の収束が見られたかどうかを判断する（ステップＳ３０４）。
【００３８】
収束していない場合には、カウンタｉの値をインクリメントし、カウンタｉの値が所定の反復回数ＩＴＬ１を超えていないかどうかの打ち切り条件を判断する（ステップＳ３０５）。そして、超えていなければ再度、ステップＳ３０３に戻り、前回の未知変数Ｘ^{（ｉ＋１）}を式３の未知変数Ｘ^（ｉ）に代入し、前回と同様にして未知変数Ｘ^{（ｉ＋１）}を計算する。この繰り返しにより、Ｎｅｗｔｏｎ法による求解処理を行う。
【００３９】
さて、本発明ではＧｍｉｎ−Ｓｔｅｐｐｉｎｇ法を採用するので、ステップＳ３０４にて未知変数Ｘ^{（ｉ＋１）}が収束するたびに、緩和値を用いて演算（具体的には除算）することにより仮想コンダクタンスＧｍｉｎの値を逓減させる。
【００４０】
まず、ステップＳ３０４にて未知変数Ｘ^{（ｉ＋１）}が収束したと判断されると、仮想コンダクタンスＧｍｉｎの値が充分に緩和されているかどうかを判断する（ステップＳ３０６）。具体的には、ステップＳ３０６に示すように、例えば緩和因子Ｇｒａｍｐの値が０．０以下となったかどうかを判定する。
【００４１】
もし、緩和因子Ｇｒａｍｐの値が０．０を上回っておれば、ステップＳ３０２において示したＧｍｉｎ^（ｊ）の値が、まだ充分には小さな値となっておらず、減少させる必要がある。これはすなわち、図２において導入した仮想抵抗Ｇｍｉｎのコンダクタンスが充分に小さな値となっておらず、本来の回路構成に付加した仮想抵抗Ｇｍｉｎの影響が未だ残置していることを意味する。
【００４２】
すなわち、ステップＳ３０６でＹｅｓと判断された場合には、カウンタｊの値をインクリメントし、仮想コンダクタンス値Ｇｍｉｎの緩和因子Ｇｒａｍｐの調整を行う（ステップＳ３０７ａ）。
【００４３】
具体的には、ステップＳ３０７ａに示すように、カウンタｋの値に応じた現在の緩和割合Ｇｒａｔｅ１^（ｋ）の値をパラメータＧｒａｔｅとし、現在の緩和因子Ｇｒａｍｐの値からパラメータＧｒａｔｅの値を差し引く処理を行って、緩和因子Ｇｒａｍｐの値を減少させる。このことはつまり、ステップＳ３０２において、仮想コンダクタンスの値Ｇｍｉｎ^（ｊ）が１０^{Ｇｒａｔｅ}という緩和値で除算され、Ｇｍｉｎ^（ｊ）の値がＧｍｉｎ０×１０^{Ｇｒａｍｐ−Ｇｒａｔｅ}に減少することを意味する。
【００４４】
なお、ここでは、緩和値１０^{Ｇｒａｔｅ}で除算することにより仮想コンダクタンスＧｍｉｎの値を逓減させる場合を示したが、逓減手法は除算に限られるものではなく、例えば減算等の他の演算であってもよい。
【００４５】
そして、再度、ステップＳ３０２にてＮｅｗｔｏｎ法のカウンタｉの値を初期値１に設定する。その後、再びステップＳ３０３〜Ｓ３０５を繰り返してＮｅｗｔｏｎ法による求解処理を行う。なお、この求解処理においては、前回のステップＳ３０４にて得られた収束解を新たな初期値として用いる。
【００４６】
そして、前回と同様に、ステップＳ３０４にて未知変数Ｘ^{（ｉ＋１）}が収束すれば、ステップＳ３０６にて緩和因子Ｇｒａｍｐの値が充分に小さな値となっているか、再度、判断する。そして、未だ緩和因子Ｇｒａｍｐの値が小さな値となっていなければ、再度、ステップＳ３０７ａにて緩和因子Ｇｒａｍｐの値を調整し、緩和値１０^{Ｇｒａｔｅ}で除算することにより仮想コンダクタンスＧｍｉｎの値を逓減させる。
【００４７】
ここでもし、緩和因子Ｇｒａｍｐの値が０．０以下となれば、ステップＳ３０２において示したＧｍｉｎ^（ｊ）の値は、第１の所定値たる仮想コンダクタンス基準値Ｇｍｉｎ０の値以下になっており、充分に小さな値であると判断される。これはすなわち、図２において導入した仮想抵抗Ｇｍｉｎのコンダクタンス値が充分に小さくなっており、本来の回路構成と同視し得る状況下で回路網方程式の解が得られたことを意味する。
【００４８】
よって、緩和因子Ｇｒａｍｐの値が０．０以下であれば、すなわちステップＳ３０６でＮｏと判断された場合には、求解が成功したと判断し、回路網方程式求解部２０はその収束解を真値として計算結果出力部３０に出力する。
【００４９】
さて、本願においては、反復解法において解が収束せず、かつ、所定の打ち切り条件が満たされたときには、仮想コンダクタンスの値の逓減に用いる緩和値を変更して求解処理を再度行う。
【００５０】
すなわち、ステップＳ３０４において未知変数Ｘ^{（ｉ＋１）}が収束せず、かつ、ステップＳ３０５においてＮｅｗｔｏｎ法の反復回数を示すカウンタｉの値が反復回数ＩＴＬ１を超えたという所定の打ち切り条件が満たされたときには、Ｇｍｉｎ−Ｓｔｅｐｐｉｎｇ法の反復回数を示すカウンタｋの値をインクリメントしつつステップＳ３０８に進む。そして、ステップＳ３０８においてカウンタｋの値が所定の反復回数Ｎｕｍｇｒを超えていなければ、ステップＳ３０１に戻り、再度、緩和因子Ｇｒａｍｐを初期値Ｇｒａｍｐ０に設定し、緩和因子Ｇｒａｍｐのカウンタｊの値を初期値１に設定する。
【００５１】
ステップＳ３０１においてはさらに、カウンタｋの値が１つ増加した分だけ前回の緩和割合Ｇｒａｔｅ１^（ｋ）の値を増加させる。すなわち、緩和割合減少率Ｇｒｉｎｃの値だけ緩和割合Ｇｒａｔｅ１^（ｋ）の値を増加させる。そして、再びステップＳ３０２〜Ｓ３０８の各ステップを繰り返すのである。
【００５２】
なお、ステップＳ３０８でカウンタｋの値が所定の反復回数Ｎｕｍｇｒを超えた場合には、緩和割合Ｇｒａｔｅ１^（ｋ）の値を変更しても解の真値が得られなかったと判断して、計算結果出力部に３０にその旨を表示する。
【００５３】
上記の各ステップＳ３００〜Ｓ３０８の各処理は、回路網方程式求解部２０たる演算処理部が行う。具体的には、ステップＳ３００におけるカウンタｋのリセット、ステップＳ３０１におけるＧｒａｍｐ初期化、カウンタｊのリセット、Ｇｒａｔｅ１^（ｋ）の設定、ステップＳ３０２におけるＧｍｉｎ^（ｊ）の設定、カウンタｉのリセット、ステップＳ３０３〜Ｓ３０５におけるＮｅｗｔｏｎ法求解処理、ステップＳ３０６におけるＧｍｉｎ^（ｊ）の緩和判定、ステップＳ３０７ａにおけるＧｍｉｎの緩和因子の調整、ステップＳ３０８におけるＧｍｉｎ−Ｓｔｅｐｐｉｎｇ法の求解失敗判定、のいずれについても回路網方程式求解部２０たる演算処理部内の中央処理装置２０ｂが、ＲＯＭ２０ｃやＲＡＭ２０ｄに格納された所定のプログラムに従って行う。
【００５４】
以上の説明において使用した各パラメータの具体例は、以下のとおりである。すなわち、例えばＧｍｉｎ０＝１×１０^−１２［Ｓ（ジーメンス）］、Ｇｒａｍｐ０＝６、Ｇｒａｔｅ０＝１．５、Ｇｒｉｎｃ＝０．１、ＩＴＬ１＝１００［回］、Ｎｕｍｇｒ＝１０［回］と設定すればよい。これらのデータは、予め回路シミュレーションのオペレーターにより設定され、回路情報記憶部１０に記憶されている。
【００５５】
これらの設定値の下では、上記処理は以下のようになる。まず、Ｇｍｉｎ−Ｓｔｅｐｐｉｎｇ法の開始当初（ｋ＝１の場合）においては、Ｇｒａｔｅ１^（ｋ）＝Ｇｒａｔｅ０＋（ｋ−１）×Ｇｒｉｎｃ＝１．５＋（１−１）×０．１＝１．５となる（ステップＳ３０１）。また、Ｇｍｉｎ^（ｊ）＝Ｇｍｉｎ０×１０^{Ｇｒａｍｐ}＝１×１０^−１２×１０^６＝１×１０^−６と設定される（ステップＳ３０２）。
【００５６】
そして、Ｎｅｗｔｏｎ法で収束解が得られれば、ステップＳ３０６においてＧｒａｍｐ＝６＞０．０と判断され、ステップＳ３０７ａに移る。ステップＳ３０７ａにおいては、ＧｒａｔｅにＧｒａｔｅ１^（ｋ）＝１．５の値が代入され、Ｇｒａｍｐの値６からＧｒａｔｅの値１．５が差し引かれる。これにより、Ｇｒａｍｐの値は４．５となる。
【００５７】
次に、ステップＳ３０２に戻るので、Ｇｍｉｎ^（ｊ）＝Ｇｍｉｎ０×１０^{Ｇｒａｍｐ}＝１×１０^−１２×１０^４．５＝１×１０^−７．５と設定される。以下、同様にしてＮｅｗｔｏｎ法で収束解が得られた場合には、Ｇｒａｍｐの値は４．５→３．０→１．５→０．０と減少していくので、Ｇｍｉｎ^（ｊ）の値も、１×１０^−７．５→１×１０^−９．０→１×１０^{−１０．５}→１×１０^{−１２．０}と減少する。そして、Ｇｒａｍｐの値が０．０に達したときに、Ｇｍｉｎ^（ｊ）の値がその基準値Ｇｍｉｎ０＝１×１０^−１２以下となって、そのときの収束解が真値として出力されることになる。
【００５８】
一方、上記処理中で収束解が得られず、かつ、ステップＳ３０５において反復回数がＩＴＬ１＝１００［回］を超えるという所定の打ち切り条件を満たしてしまった場合には、ｋ＝２とされ、ステップＳ３０８にてｋ＝２＜Ｎｕｍｇｒ＝１０［回］と判断された上でステップＳ３０１に戻る。この場合、Ｇｒａｔｅ１^（ｋ）＝Ｇｒａｔｅ０＋（ｋ−１）×Ｇｒｉｎｃ＝１．５＋（２−１）×０．１＝１．６となる（ステップＳ３０１）。また、Ｇｍｉｎ^（ｊ）については前回と同様１×１０^−６と設定される（ステップＳ３０２）。
【００５９】
そして、Ｎｅｗｔｏｎ法で収束解が得られれば、ステップＳ３０６においてＧｒａｍｐ＝６＞０．０と判断され、ステップＳ３０７ａに移る。ステップＳ３０７ａにおいては、ＧｒａｔｅにＧｒａｔｅ１^（ｋ）＝１．６の値が代入され、Ｇｒａｍｐの値６からＧｒａｔｅの値１．６が差し引かれる。これにより、Ｇｒａｍｐの値は４．４となる。
【００６０】
次に、ステップＳ３０２に戻るので、Ｇｍｉｎ^（ｊ）＝Ｇｍｉｎ０×１０^{Ｇｒａｍｐ}＝１×１０^−１２×１０^４．４＝１×１０^−７．６と設定される。以下、同様にしてＮｅｗｔｏｎ法で収束解が得られた場合には、Ｇｒａｍｐの値は４．４→２．８→１．２→−０．４と減少していくので、Ｇｍｉｎ^（ｊ）の値も、１×１０^−７．６→１×１０^−９．２→１×１０^{−１０．８}→１×１０^{−１２．４}と減少する。そして、Ｇｒａｍｐの値が−０．４に達したときに、Ｇｍｉｎ^（ｊ）の値がその基準値Ｇｍｉｎ０＝１×１０^−１２以下となって、そのときの収束解が真値として出力されることになる。
【００６１】
このように、上記の数値例においては、ｋ＝１の場合、解が収束するたびに、緩和値１０^{Ｇｒａｔｅ}＝１０^１．５で除算することにより仮想コンダクタンスＧｍｉｎの値を逓減させるが、ｋ＝２の場合は、解が収束するたびに、緩和値１０^{Ｇｒａｔｅ}＝１０^１．６で除算することにより仮想コンダクタンスＧｍｉｎの値を逓減させる。そして、３回目以降については、緩和値を１０^{Ｇｒａｔｅ}＝１０^１．７、１０^１．８、１０^１．９…として仮想コンダクタンスＧｍｉｎの値を除算することとなる。
【００６２】
すなわち、本実施の形態に係る回路シミュレーション方法および回路シミュレーション装置によれば、仮想コンダクタンスＧｍｉｎの値が充分に小さな値とならず、かつ、解が収束しない場合には、仮想コンダクタンスＧｍｉｎの緩和値が自動的に変更されて再度、回路シミュレーションが行われることになる。
【００６３】
これにより緩和値の再設定という煩瑣な作業を省くことが可能となり、従来、回路シミュレーションのオペレーターに強いられていた逓減手法の見直しの負担が軽減される。また、緩和法により求解処理を行う場合、緩和値を変更することにより求解可能性が拡大することがある。そのため、本実施の形態に係る回路シミュレーション方法および回路シミュレーション装置によれば、回路網方程式の求解処理にて解が求めやすくなる。
【００６４】
なお、本願発明の射程は、本実施の形態に係る回路シミュレーション方法の各ステップをコンピュータに実行させる回路シミュレーションプログラムにも及ぶ。
【００６５】
＜実施の形態２＞
本実施の形態は、実施の形態１に係る回路シミュレーション方法、回路シミュレーション装置および回路シミュレーションプログラムの変形例であって、実施の形態１におけるステップＳ３０７ａにおいて、仮想コンダクタンスＧｍｉｎの値が所定値よりも小さくなったときに、緩和値を所定の固定値に変更しつつ、変更後の緩和値で仮想コンダクタンスの値を逓減させるようにしたものである。
【００６６】
図５は、本実施の形態に係る回路シミュレーション装置および回路シミュレーション方法を示す図である。なお、図５においては、ステップＳ３０７ａがステップＳ３０７ｂに変更されている点以外、装置構成および各ステップは図３と同じである。
【００６７】
ステップＳ３０７ｂについて説明する。図５に示すように、このステップＳ３０７ｂにおいては、緩和因子Ｇｒａｍｐの値が、予め設定したしきい値Ｇｔｒａｎよりも大きいときは、実施の形態１の場合と同様、カウンタｋの値に応じた現在の緩和割合Ｇｒａｔｅ１^（ｋ）の値をパラメータＧｒａｔｅとし、現在の緩和因子Ｇｒａｍｐの値からパラメータＧｒａｔｅの値を差し引く処理を行って、緩和因子Ｇｒａｍｐの値を減少させる。
【００６８】
一方、緩和因子Ｇｒａｍｐの値がしきい値Ｇｔｒａｎ以下となったときには、すなわち、仮想コンダクタンスＧｍｉｎの値が、第２の所定値たるＧｍｉｎ０×１０^{Ｇｔｒａｎ}以下となったときには、Ｇｒａｔｅ１^（ｋ）の値をパラメータＧｒａｔｅとするのではなく、予め設定した固定緩和割合Ｇｒａｔｅ２をパラメータＧｒａｔｅとし、現在の緩和因子Ｇｒａｍｐの値からパラメータＧｒａｔｅの値を差し引く処理を行って、緩和因子Ｇｒａｍｐの値を減少させる。すなわち、この場合はステップＳ３０１での緩和割合Ｇｒａｔｅ１^（ｋ）の再設定を行わない。なお、もちろん第２の所定値たるＧｍｉｎ０×１０^{Ｇｔｒａｎ}の値は、仮想コンダクタンス基準値Ｇｍｉｎ０よりも大きく設定される。
【００６９】
これにより、緩和値１０^{Ｇｒａｔｅ}の値が所定の固定値１０^{Ｇｒａｔｅ２}に変更され、変更後の緩和値１０^{Ｇｒａｔｅ２}で除算することにより仮想コンダクタンスＧｍｉｎの値が逓減される。なお、ここでも、変更後の緩和値１０^{Ｇｒａｔｅ２}で除算することにより仮想コンダクタンスＧｍｉｎの値を逓減させる場合を示したが、逓減手法は除算に限られるものではなく、減算等の他の演算であってもよい。
【００７０】
その他の点については、実施の形態１に係る回路シミュレーション方法、回路シミュレーション装置および回路シミュレーションプログラムと同様のため、説明を省略する。
【００７１】
なお、しきい値Ｇｔｒａｎおよび固定緩和割合Ｇｒａｔｅ２の具体例は、以下のとおりである。すなわち、例えばＧｔｒａｎ＝４．０、Ｇｒａｔｅ２＝１．０と設定すればよい。これらのデータも、予め回路シミュレーションのオペレーターにより設定され、回路情報記憶部１０に記憶されている。
【００７２】
これらの設定値の下では、実施の形態１にて用いた数値例をも援用すれば、上記処理は以下のようになる。
【００７３】
実施の形態１では、ｋ＝１の場合において、Ｇｒａｍｐの値は６．０→４．５→３．０→１．５→０．０と減少していくので、Ｇｍｉｎ^（ｊ）の値も、１×１０^−６．０→１×１０^−７．５→１×１０^−９．０→１×１０^{−１０．５}→１×１０^{−１２．０}と減少していた。しかし、本実施の形態では、Ｇｒａｍｐの値がＧｔｒａｎ＝４．０以下となったときには、ＧｒａｔｅがＧｒａｔｅ２＝１．０に固定されるので、Ｇｒａｍｐの値は６．０→４．５→３．０→２．０→１．０→０．０と減少し、Ｇｍｉｎ^（ｊ）の値も、１×１０^−６．０→１×１０^−７．５→１×１０^−９．０→１×１０^{−１０．０}→１×１０^{−１１．０}→１×１０^{−１２．０}と減少することになる。
【００７４】
ｋ＝２の場合も同様に、Ｇｒａｍｐの値がＧｔｒａｎ＝４．０以下となったときにＧｒａｔｅがＧｒａｔｅ２＝１．０に固定されるので、Ｇｒａｍｐの値は６．０→４．４→２．８→１．８→０．８→−０．２と減少し、Ｇｍｉｎ^（ｊ）の値も、１×１０^−６．０→１×１０^−７．６→１×１０^−９．２→１×１０^{−１０．２}→１×１０^{−１１．２}→１×１０^{−１２．２}と減少することになる。ｋ＝３以降の場合も同様の処理となる。
【００７５】
本実施の形態によれば、仮想コンダクタンスＧｍｉｎの値が第２の所定値たるＧｍｉｎ０×１０^{Ｇｔｒａｎ}以下となったときには、緩和値１０^{Ｇｒａｔｅ}の値を所定の固定値１０^{Ｇｒａｔｅ２}に変更して、変更後の緩和値で除算等の演算を行うことにより仮想コンダクタンスの値Ｇｍｉｎを逓減させ、求解処理を行う。
【００７６】
よって、実施の形態１におけるように、緩和割合Ｇｒａｔｅ１^（ｋ）の値を１．５（ｋ＝１の場合）や１．６（ｋ＝２の場合）と設定して、緩和値１０^{Ｇｒａｔｅ}の値を大きく設定しておき、一方、固定緩和割合Ｇｒａｔｅ２を１．０と設定して、所定の固定値１０^{Ｇｒａｔｅ２}を小さく設定しておけば、求解処理の初期段階では仮想コンダクタンスの値を大幅に変更して解の追跡効率を上げることができ、一方、真値に近づいた求解処理の最終段階では仮想コンダクタンスの値を細やかに変更して精度よく真値を求めることが可能となる。
【００７７】
＜実施の形態３＞
本実施の形態も、実施の形態１に係る回路シミュレーション方法、回路シミュレーション装置および回路シミュレーションプログラムの変形例であって、実施の形態１におけるステップＳ３０７ａにおいて、乱数に基づいて発生させた値を緩和値に対して演算しつつ、演算後の緩和値で除算等することにより仮想コンダクタンスの値を逓減させるようにしたものである。
【００７８】
図６は、本実施の形態に係る回路シミュレーション装置および回路シミュレーション方法を示す図である。なお、図６においては、ステップＳ３０７ａがステップＳ３０７ｃに変更されている点以外、装置構成および各ステップは図３と同じである。
【００７９】
ステップＳ３０７ｃについて説明する。図６に示すように、このステップＳ３０７ｃにおいては、カウンタｋの値に応じた現在の緩和割合Ｇｒａｔｅ１^（ｋ）に、乱数ｒａｎｄ（）を加えた値をパラメータＧｒａｔｅとし、現在の緩和因子Ｇｒａｍｐの値からパラメータＧｒａｔｅの値を差し引く処理を行って、緩和因子Ｇｒａｍｐの値を減少させる。なお、乱数ｒａｎｄ（）は、発生範囲に上下限のない任意の値でもよいが、例えば０≦ｒａｎｄ（）≦１のように所定の範囲内の任意の値と制限してもよい。
【００８０】
このことはつまり、緩和値を用いた演算の都度、ステップＳ３０２において、乱数ｒａｎｄ（）に基づいて発生させた値１０^{ｒａｎｄ（）}を１０^{Ｇｒａｔｅ１（ｋ）}という緩和値に対して乗算しつつ、演算後の緩和値１０^{Ｇｒａｔｅ１（ｋ）＋ｒａｎｄ（）}で除算して仮想コンダクタンスＧｍｉｎ^（ｊ）の値を逓減させることを意味する。
【００８１】
なお、上記においては、乱数ｒａｎｄ（）に基づいて発生させた値１０^{ｒａｎｄ（）}を緩和値１０^{Ｇｒａｔｅ１（ｋ）}に対して乗算する場合を示したが、その他にも加算、減算または除算等の演算を行ってもよい。
【００８２】
また、上記においては、演算後の緩和値１０^{Ｇｒａｔｅ１（ｋ）＋ｒａｎｄ（）}で除算することにより仮想コンダクタンスＧｍｉｎの値を逓減させる場合を示したが、逓減手法は除算に限られるものではなく、減算等の他の演算であってもよい。
【００８３】
その他の点については、実施の形態１に係る回路シミュレーション方法、回路シミュレーション装置および回路シミュレーションプログラムと同様のため、説明を省略する。
【００８４】
本実施の形態によれば、乱数ｒａｎｄ（）に基づいて発生させた値１０^{ｒａｎｄ（）}を緩和値１０^{Ｇｒａｔｅ１（ｋ）}に対して演算しつつ、演算後の緩和値１０^{Ｇｒａｔｅ１（ｋ）＋ｒａｎｄ（）}で仮想コンダクタンスＧｍｉｎの値を逓減させる。よって、緩和値をランダムに変更することが可能となり、求解可能性が拡大することがある。
【００８５】
なお、本実施の形態において、カウンタｋのインクリメント、ステップＳ３０８でのカウンタｋの値の判断、およびステップＳ３０１での緩和割合Ｇｒａｔｅ１^（ｋ）の再設定、のいずれをも行わないようにしてもよい。その場合、Ｇｍｉｎ−Ｓｔｅｐｐｉｎｇ法における緩和値の再設定を行わないことになる。本実施の形態では、緩和値を用いた演算の都度、乱数に基づいて発生させた値により緩和値をランダムに変更する点に特徴があるので、そのような緩和値の再設定を行わない場合も本願発明の射程に含まれる。
【００８６】
＜変形例＞
上記実施の形態１乃至３においては、ステップＳ３０３〜Ｓ３０５における反復解法としてＮｅｗｔｏｎ法を採用していた。しかしながら、上記特許文献１にてソルバの他の例として挙げられているように、反復解法にはＮｅｗｔｏｎ法の他にもＤａｍｐｅｄ−Ｎｅｗｔｏｎ法やホモトピー法等の手法がある。
【００８７】
よって、上記実施の形態１乃至３において、Ｎｅｗｔｏｎ法に代わって、これらＤａｍｐｅｄ−Ｎｅｗｔｏｎ法やホモトピー法等、他の反復解法を採用してもよい。そうすれば、シミュレーション対象たる回路に適した反復解法を選択することができ、その場合も上記と同様の効果が得られる。
【００８８】
また、上記特許文献１に記載の回路シミュレーション装置においては、選択可能なソルバの一つとして通常のＧｍｉｎ−Ｓｔｅｐｐｉｎｇ法が挙げられているが、通常のＧｍｉｎ−Ｓｔｅｐｐｉｎｇ法に代えて本願に記載のＧｍｉｎ−Ｓｔｅｐｐｉｎｇ法を採用するようにしてもよい。
【００８９】
【発明の効果】
請求項１に記載の発明によれば、反復解法において解が収束せず、かつ、所定の打ち切り条件が満たされたときは、緩和値を変更して求解処理を再度、行う。よって、Ｇｍｉｎ−Ｓｔｅｐｐｉｎｇ法を行うに際して緩和値を再入力する手間が省け、回路シミュレーションのオペレーターに強いられていた逓減手法の見直しの負担が軽減される。また、緩和法により求解処理を行う場合、緩和値を変更することにより求解可能性が拡大することがある。そのため、請求項１に記載の発明によれば、回路網方程式の求解処理にて解が求めやすくなる。
【００９０】
請求項５に記載の発明によれば、緩和値を用いた演算の都度、乱数に基づいて発生させた値により緩和値をランダムに変更する。よって、求解可能性が拡大することがある。
【図面の簡単な説明】
【図１】シミュレーション対象たる回路の一例の一部分を示す図である。
【図２】Ｇｍｉｎ−Ｓｔｅｐｐｉｎｇ法において回路内の所定箇所に導入される仮想抵抗Ｇｍｉｎを示す図である。
【図３】実施の形態１に係る回路シミュレーション装置および回路シミュレーション方法を示す図である。
【図４】実施の形態１に係る回路シミュレーション装置の詳細構成を示す図である。
【図５】実施の形態２に係る回路シミュレーション装置および回路シミュレーション方法を示す図である。
【図６】実施の形態３に係る回路シミュレーション装置および回路シミュレーション方法を示す図である。
【符号の説明】
１０ 回路情報記憶部、２０ 回路網方程式求解部、３０ 計算結果出力部。[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a circuit simulation method, a circuit simulation device, and a circuit simulation program used in a semiconductor integrated circuit design process.
[0002]
[Prior art]
The manufacturing process of a semiconductor integrated circuit includes a design process of designing the circuit and a semiconductor process process of realizing the circuit as a semiconductor device based on information obtained in the design process. Then, in the design process, a circuit simulation using a computer is performed to predict the function and operation of the semiconductor integrated circuit.
[0003]
In circuit simulation, creation of a network equation and device modeling are performed. Creating a network equation refers to establishing an equation that uses the values of current and voltage in each part in the circuit as solutions based on information on elements included in the circuit and their connection relationships. Device modeling refers to replacing a device whose electric characteristics are non-linear, such as a diode or a transistor, with a model that can be easily simulated (for example, a linear model).
[0004]
Prior art document information related to the invention of this application includes the following.
[0005]
[Patent Document 1]
JP-A-9-179895
[Patent Document 2]
JP-A-7-295959
[Patent Document 3]
JP-A-10-198654
[0006]
[Problems to be solved by the invention]
For example, in the above-mentioned Patent Document 1, when solving a network equation, various solvers (such as a Newton method or a Damped-Newton method), which are a kind of an iterative solution method, for solving a network equation are used in accordance with the convergence of the solution. This describes a technique for performing a circuit simulation while switching between solution methods.
[0007]
This application focuses on the Gmin-Stepping method among the various solvers described above. As described in Patent Document 1, in the Gmin-Stepping method, a pn junction existing in each part such as between a source and a substrate of a MOSFET is regarded as a diode, and a virtual resistor having a virtual conductance is connected in parallel to the diode. insert. Thereby, the non-linearity of the electric characteristics of the element including the pn junction is reduced, and the convergence of the solution is improved.
[0008]
In the Gmin-Stepping method, the value of the virtual conductance is set to a predetermined initial value, and the solution calculation process is started by an iteration method such as the Newton method. When the solution converges, the value of the virtual conductance is gradually reduced, and the solution calculation process is performed again. Then, such processing is repeated.
[0009]
Specifically, at the time of the first circuit simulation, the value of the virtual conductance is set to a certain value, and if the solution converges by the solution processing, the value of the virtual conductance is set to a value smaller than the previous value at the time of the second circuit simulation. Change and perform the solution process again. Thereafter, the value of the virtual conductance is reduced in the same manner, and the solution processing is performed. In this way, the virtual conductance is gradually changed to a small value, so as to gradually approach the original open state (the original circuit configuration not including the virtual resistor).
[0010]
Now, in the conventional Gmin-Stepping method, since the value of the virtual conductance is reduced as described above, there are the following problems.
[0011]
In other words, the specific method of decreasing the virtual conductance is empirically determined by the operator of the circuit simulation, and an appropriate decreasing method is not always adopted. If an appropriate diminishing method is not adopted, the computation time alone increases, and the solution often does not converge. Therefore, in such a case, it is necessary to reset the step-down method and perform the circuit simulation again.
[0012]
That is, the conventional Gmin-Stepping method has forced the operator of the circuit simulation to perform a complicated work of reviewing the step-down method.
[0013]
The present invention has been made in view of the above circumstances, and a circuit simulation method, a circuit simulation apparatus, and a circuit simulation that reduce the burden of reviewing the step-down method imposed on a circuit simulation operator when performing a Gmin-Stepping method To provide a program.
[0014]
[Means for Solving the Problems]
According to the first aspect of the present invention, there is provided (a) a virtual conductance used for creating a network equation for a circuit specified by circuit information, a relaxation value used for changing the virtual conductance, and the network equation. (B) introducing a virtual resistor having the virtual conductance into a portion of the circuit that satisfies a predetermined condition, based on the circuit information. And (c) causing the computer to perform an arithmetic process on the circuit network equation created in step (b) using an iterative solution until the solution converges. (D) using the relaxation value each time the solution converges in step (c). And causing the computer to calculate and reduce the value of the virtual conductance, and adopt the converged solution as a new initial value of the iterative solution to perform the steps (b) and (c). And (e) determining the converged solution as a true value when the value of the virtual conductance is equal to or less than a first predetermined value in the step (d); A circuit simulation method in which, when the solution does not converge and a predetermined termination condition is satisfied, the relaxation value set in the step (a) is changed and the step (b) and the subsequent steps are performed. .
[0015]
According to a fifth aspect of the present invention, there is provided (a) a virtual conductance used for creating a network equation for a circuit specified by circuit information, a relaxation value used for changing the virtual conductance, and the network equation. (B) introducing a virtual resistor having the virtual conductance into a portion of the circuit that satisfies a predetermined condition, based on the circuit information. And (c) causing the computer to perform an arithmetic process on the circuit network equation created in step (b) using an iterative solution until the solution converges. (D) using the relaxation value each time the solution converges in step (c). And causing the computer to calculate and reduce the value of the virtual conductance, and adopt the converged solution as a new initial value of the iterative solution to perform the steps (b) and (c). And (e) judging the converged solution as a true value when the value of the virtual conductance is equal to or less than a first predetermined value in the step (d); A circuit simulation method for randomly changing the relaxation value with a value generated based on a random number each time an operation using the relaxation value is performed.
[0016]
BEST MODE FOR CARRYING OUT THE INVENTION
<Embodiment 1>
In the present embodiment, when performing the Gmin-Stepping method using a computer, when the solution does not converge in the iterative solution and a predetermined truncation condition is satisfied, the relaxation value used for gradually decreasing the virtual conductance is changed. A circuit simulation method, a circuit simulation device, and a circuit simulation program for performing a solution process again.
[0017]
FIG. 1 is a diagram illustrating a part of an example of a circuit to be simulated. As shown in FIG. 1, this circuit includes, for example, resistors Ra to Rc and a diode Da. Among them, the diode Da may be either a diode as an element, or a diode assuming a pn junction existing in each part such as between the source and the substrate of the MOSFET as described above. In FIG. 1, one end of each of the resistors Ra to Rc and the anode of the diode Da are connected at a node Na.
[0018]
FIG. 2 is a diagram illustrating a virtual resistor Gmin introduced at a predetermined position in a circuit in the Gmin-Stepping method. As shown in FIG. 2, the virtual resistor Gmin is introduced in parallel with the diode Da.
[0019]
FIG. 3 is a diagram showing a circuit simulation device and a circuit simulation method according to the present embodiment. FIG. 4 is a diagram showing a detailed configuration of the circuit simulation apparatus according to the present embodiment. FIG. 3 shows that a computer as a circuit simulation apparatus according to the present embodiment includes a circuit information storage unit 10, a circuit network equation solving unit 20, and a calculation result output unit 30. It is also shown that the circuit solving method according to the present embodiment including steps S300 to S308 is performed in the solving unit 20.
[0020]
The circuit information storage unit 10 is a storage device such as a hard disk that stores information on a circuit to be simulated (information on elements included in the circuit and their connection relations).
[0021]
As shown in FIG. 4, the circuit network equation solving unit 20 is an arithmetic processing unit including an input / output interface 20a, a central processing unit 20b, a ROM 20c, a RAM 20d, and the like, and a predetermined software program stored in the ROM 20c or the RAM 20d. Work by. The input / output interface 20a, the ROM 20c, and the RAM 20d are all connected to and controlled by the central processing unit 20b. The circuit information storage unit 10 and the calculation result output unit 30 are connected to the input / output interface 20a. The network equation solving unit 20 creates a network equation as, for example, a simultaneous nonlinear equation based on the circuit information data obtained from the circuit information storage unit 10. Then, a solution process of the created network equation is performed.
[0022]
The calculation result output unit 30 is an output unit including a display, a printer, and the like, for outputting a simulation result in the circuit network equation solving unit 20.
[0023]
The circuit equation created in the circuit equation solving section 20 is represented by the following equation (1).
[0024]
(Equation 1)

[0025]
Here, X is an unknown variable containing as parameters the voltage at each node and the current flowing through each branch. R indicates that each parameter of the unknown variable X is a real number, and n indicates the number of parameters. Gmin is a parameter indicating the value of the virtual conductance at the virtual resistor Gmin.
[0026]
Hereinafter, creation and solution processing of the network equation in the network equation solving section 20 will be described. In FIG. 3, the processing items in each step are shown, and the instruction formula based on the C language notation is also shown in [].
[0027]
First, the value of a counter k that defines the number of changes of the relaxation value used for the calculation in the Gmin-Stepping method is set to an initial value 1 (step S300). Note that the relaxation value is a value used for an operation for reducing the virtual conductance.
[0028]
Next, the relaxation factor Gramp of the virtual conductance Gmin is set to the initial value Gramp0. The relaxation factor Gramp is 10 ^Gramp Is a parameter that relaxes the value of the virtual conductance Gmin by multiplying the virtual conductance reference value Gmin0 in the form of
[0029]
Also, the value of a counter j that counts the number of times the relaxation factor Gramp is changed per Gmin-Stepping process is set to an initial value 1. Furthermore, the relaxation rate of virtual conductance Gmin, Rate1, ^(K) Is set using the initial value of the relaxation rate, Rate0, the counter k, and the reduction rate of the relaxation rate Grinc (step S301). In addition, the relaxation ratio Rate1 ^(K) Is, specifically, as shown in FIG. ^(K) = Grate0 + (k-1) × Grinc.
[0030]
In the Newton method, the unknown variable X is sequentially updated. In the Gmin-Stepping method, the value of the virtual conductance Gmin is gradually reduced. Therefore, Expression 1 above is expressed as Expression 2 below using a counter j and a counter i for defining the number of iterations of the Newton method.
[0031]
(Equation 2)

[0032]
Therefore, the virtual conductance Gmin ^(J) Is set to a predetermined initial value using the values of the virtual conductance reference value Gmin0 and the relaxation factor Gramp. Then, the value of the counter i is set to the initial value 1. Further, the solution (= unknown variable) X of the network equation in the Newton method is set to a predetermined initial value (for example, voltages V1, V2,..., Etc.) (step S302). Note that the virtual conductance Gmin ^(J) Is, specifically, as shown in FIG. ^(J) = Gmin0 × 10 ^Gramp Is set.
[0033]
After the above settings, the above equation 2 is created and solved by the Newton method. In the Newton method, the unknown variable X is sequentially updated, and a calculation based on the following Expression 3 is performed. Equation 3 shows the solution at the (i + 1) -th iteration. As shown in step S302, the initial value of the solution X when i = 1 is set in advance by the operator of the circuit simulation.
[0034]
[Equation 3]

[0035]
That is, by sequentially obtaining the value of the (i + 1) th unknown variable X based on the value of the i-th unknown variable X, a solution calculation process that approaches a true solution satisfying Expression 2 is performed. Then, if the obtained variation of the unknown variable X falls within a predetermined allowable error range, it is considered that the solution of the unknown variable X has converged and a true value has been obtained, and the calculation is terminated. On the other hand, if the variation of the unknown variable X does not fall within the range of the allowable error even when the specified number of iterations is reached, the solution of the unknown variable X does not converge as a predetermined censoring condition is satisfied and a true value is obtained. It is considered that it has not been performed, and the calculation ends.
[0036]
The solution processing by the Newton method is as described above, and is realized by the steps S303 to S305 in FIG. That is, first, Formula 2 is created based on the circuit information data. Then, the unknown variable X in the left side of Equation 2 ^(I) Is substituted for the i-th solution (initial value when i = 1), and F (X ^(I) , Gmin ^(J) ), And also the Jacobian ∂F / ∂X, so that the (i + 1) -th unknown variable X ^{(I + 1)} Is calculated (step S303).
[0037]
And the obtained unknown variable X ^{(I + 1)} And the i-th solution X ^(I) Is calculated based on whether the difference falls within a tolerance set in advance by an operator of the circuit simulation. ^{(I + 1)} It is determined whether or not convergence is observed (step S304).
[0038]
If not converged, the value of the counter i is incremented, and a termination condition is determined as to whether the value of the counter i does not exceed a predetermined number of iterations ITL1 (step S305). If not, the process returns to step S303 again, and the last unknown variable X ^{(I + 1)} To the unknown variable X in Equation 3. ^(I) To the unknown variable X ^{(I + 1)} Is calculated. By this repetition, a solution processing by the Newton method is performed.
[0039]
Now, in the present invention, since the Gmin-Stepping method is adopted, the unknown variable X ^{(I + 1)} Each time is converged, the value of the virtual conductance Gmin is gradually reduced by performing an operation (specifically, division) using the relaxation value.
[0040]
First, in step S304, the unknown variable X ^{(I + 1)} Is determined to have converged, it is determined whether the value of the virtual conductance Gmin is sufficiently relaxed (step S306). Specifically, as shown in step S306, for example, it is determined whether or not the value of the relaxation factor Gramp has become 0.0 or less.
[0041]
If the value of the relaxation factor Gramp is greater than 0.0, Gmin shown in step S302 ^(J) Is not yet small enough and needs to be reduced. This means that the conductance of the virtual resistor Gmin introduced in FIG. 2 does not have a sufficiently small value, and the effect of the virtual resistor Gmin added to the original circuit configuration still remains.
[0042]
That is, when it is determined as Yes in step S306, the value of the counter j is incremented, and the relaxation factor Gramp of the virtual conductance value Gmin is adjusted (step S307a).
[0043]
More specifically, as shown in step S307a, the current relaxation ratio Rate1 according to the value of the counter k ^(K) Is set as the parameter Grate, and a process of subtracting the value of the parameter Grate from the current value of the relaxation factor Gramp is performed to decrease the value of the relaxation factor Gramp. This means that in step S302, the value Gmin of the virtual conductance ^(J) Is 10 ^Grate Gmin ^(J) Is Gmin0 × 10 ^Gramp-Grate Means to decrease.
[0044]
Here, the relaxation value is 10 ^Grate Although the case where the value of the virtual conductance Gmin is gradually reduced by dividing by the above expression, the method of decreasing is not limited to the division but may be another operation such as subtraction.
[0045]
Then, the value of the counter i of the Newton method is set to the initial value 1 again in step S302. After that, steps S303 to S305 are repeated again to perform a solution process by the Newton method. In this solution processing, the convergent solution obtained in the previous step S304 is used as a new initial value.
[0046]
Then, as in the previous case, the unknown variable X is determined in step S304. ^{(I + 1)} Is converged, it is determined again in step S306 whether the value of the relaxation factor Gramp is a sufficiently small value. If the value of the relaxation factor Gramp is not yet a small value, the value of the relaxation factor Gramp is adjusted again in step S307a, and the relaxation value 10 ^Grate To reduce the value of the virtual conductance Gmin.
[0047]
Here, if the value of the relaxation factor Gramp becomes 0.0 or less, Gmin shown in step S302 ^(J) Is less than or equal to the first predetermined value, the virtual conductance reference value Gmin0, and is determined to be a sufficiently small value. This means that the conductance value of the virtual resistor Gmin introduced in FIG. 2 is sufficiently small, and a solution of the circuit network equation has been obtained under a condition that can be regarded as the same as the original circuit configuration.
[0048]
Therefore, if the value of the relaxation factor Gramp is equal to or less than 0.0, that is, if No is determined in step S306, it is determined that the solution is successful, and the circuit equation solving unit 20 determines the converged solution as a true value. Is output to the calculation result output unit 30.
[0049]
Now, in the present application, when the solution does not converge in the iterative solution and a predetermined cutoff condition is satisfied, the relaxation value used for gradually decreasing the value of the virtual conductance is changed and the solution calculation process is performed again.
[0050]
That is, in step S304, the unknown variable X ^{(I + 1)} Does not converge, and in step S305, when the predetermined discontinuation condition that the value of the counter i indicating the number of iterations of the Newton method has exceeded the number of iterations ITL1 is satisfied, the counter k indicating the number of iterations of the Gmin-Stepping method The process proceeds to step S308 while incrementing the value of. If the value of the counter k does not exceed the predetermined number of repetitions Numgr in step S308, the process returns to step S301, sets the relaxation factor Gramp to the initial value Gramp0 again, and sets the value of the counter j of the relaxation factor Gramp to the initial value. Set to 1.
[0051]
In step S301, the previous relaxation rate Rate1 is increased by the increment of the value of the counter k by one. ^(K) Increase the value of. That is, the relaxation rate Rate1 is reduced by the value of the relaxation rate reduction rate Grinc. ^(K) Increase the value of. Then, the steps S302 to S308 are repeated again.
[0052]
If the value of the counter k has exceeded the predetermined number of repetitions Numgr in step S308, the relaxation rate Rate1 ^(K) It is determined that the true value of the solution has not been obtained even if the value has been changed, and that fact is displayed on the calculation result output unit 30.
[0053]
The processing of each of the above steps S300 to S308 is performed by the arithmetic processing unit as the circuit network equation solving unit 20. Specifically, reset of the counter k in step S300, initialization of Gramp in step S301, reset of the counter j, and Grate1 ^(K) , Gmin in step S302 ^(J) , Resetting the counter i, Newton's method solution processing in steps S303 to S305, Gmin in step S306 ^(J) , The adjustment of the Gmin mitigation factor in step S307a, and the failure determination of the Gmin-Stepping method in step S308, the central processing unit 20b in the arithmetic processing unit as the circuit network equation solving unit 20 uses the ROM 20c or the RAM 20d. In accordance with a predetermined program stored in the.
[0054]
Specific examples of each parameter used in the above description are as follows. That is, for example, Gmin0 = 1 × 10 ^-12 [S (Siemens)], Gramp0 = 6, Rate0 = 1.5, Grinc = 0.1, ITL1 = 100 [times], and Numgr = 10 [times]. These data are set in advance by a circuit simulation operator and stored in the circuit information storage unit 10.
[0055]
Under these setting values, the above processing is as follows. First, at the beginning of the Gmin-Stepping method (when k = 1), ^(K) = Grate0 + (k-1) * Grinc = 1.5 + (1-1) * 0.1 = 1.5 (step S301). Gmin ^(J) = Gmin0 × 10 ^Gramp = 1 × 10 ^-12 × 10 ⁶ = 1 × 10 ^-6 Is set (step S302).
[0056]
If a convergence solution is obtained by the Newton method, it is determined that Gramp = 6> 0.0 in step S306, and the process proceeds to step S307a. In step S307a, “Grate1” is added to “Grate”. ^(K) = 1.5 is substituted, and the value of Grate 1.5 is subtracted from the value of Gramp 6. Thereby, the value of Gramp becomes 4.5.
[0057]
Next, returning to step S302, Gmin ^(J) = Gmin0 × 10 ^Gramp = 1 × 10 ^-12 × 10 ^4.5 = 1 × 10 ^-7.5 Is set. Hereinafter, when a converged solution is obtained by the Newton's method in the same manner, the value of Gramp decreases from 4.5 → 3.0 → 1.5 → 0.0. ^(J) Is also 1 × 10 ^-7.5 → 1 × 10 ^-9.0 → 1 × 10 ^-10.5 → 1 × 10 ^-12.0 And decrease. When the value of Gramp reaches 0.0, Gmin ^(J) Is the reference value Gmin0 = 1 × 10 ^-12 In the following, the convergent solution at that time is output as a true value.
[0058]
On the other hand, if a convergence solution is not obtained during the above processing and if the predetermined termination condition that the number of repetitions exceeds ITL1 = 100 [times] is satisfied in step S305, k is set to 2 and k is set to 2. After it is determined in S308 that k = 2 <Numgr = 10 [times], the process returns to step S301. In this case, Grate1 ^(K) = Grate0 + (k-1) * Grinc = 1.5 + (2-1) * 0.1 = 1.6 (step S301). Gmin ^(J) About 1 × 10 as before ^-6 Is set (step S302).
[0059]
If a convergent solution is obtained by the Newton method, it is determined that Gramp = 6> 0.0 in step S306, and the process proceeds to step S307a. In step S307a, “Grate1” is added to “Grate”. ^(K) = 1.6 is substituted and the value of Grate 1.6 is subtracted from the value of Gramp 6. Thereby, the value of Gramp becomes 4.4.
[0060]
Next, returning to step S302, Gmin ^(J) = Gmin0 × 10 ^Gramp = 1 × 10 ^-12 × 10 ^4.4 = 1 × 10 ^-7.6 Is set. Hereinafter, when a converged solution is obtained by the Newton's method in the same manner, the value of Gramp decreases from 4.4 → 2.8 → 1.2 → −0.4. ^(J) Is also 1 × 10 ^-7.6 → 1 × 10 ^-9.2 → 1 × 10 ^-10.8 → 1 × 10 ^-12.4 And decrease. When the value of Gramp reaches −0.4, Gmin ^(J) Is the reference value Gmin0 = 1 × 10 ^-12 In the following, the convergent solution at that time is output as a true value.
[0061]
Thus, in the above numerical example, when k = 1, every time the solution converges, the relaxation value 10 ^Grate = 10 ^1.5 , The value of the virtual conductance Gmin is gradually reduced. However, when k = 2, the relaxation value 10 ^Grate = 10 ^1.6 To reduce the value of the virtual conductance Gmin. For the third and subsequent times, the relaxation value is 10 ^Grate = 10 ^1.7 , 10 ^1.8 , 10 ^1.9 .. Will be divided by the value of the virtual conductance Gmin.
[0062]
That is, according to the circuit simulation method and the circuit simulation apparatus according to the present embodiment, if the value of virtual conductance Gmin is not a sufficiently small value and the solution does not converge, the relaxation value of virtual conductance Gmin is reduced. The circuit is automatically changed and the circuit simulation is performed again.
[0063]
As a result, the complicated work of resetting the relaxation value can be omitted, and the burden of reviewing the step-down method conventionally imposed on the operator of the circuit simulation is reduced. In the case where the solution processing is performed by the relaxation method, the possibility of solution may be expanded by changing the relaxation value. Therefore, according to the circuit simulation method and the circuit simulation apparatus according to the present embodiment, it is easy to obtain a solution in the process of solving the network equation.
[0064]
The range of the present invention extends to a circuit simulation program that causes a computer to execute each step of the circuit simulation method according to the present embodiment.
[0065]
<Embodiment 2>
This embodiment is a modification of the circuit simulation method, the circuit simulation device, and the circuit simulation program according to the first embodiment. In step S307a in the first embodiment, the value of the virtual conductance Gmin is smaller than a predetermined value. When this happens, the value of the virtual conductance is gradually reduced with the changed relaxation value while changing the relaxation value to a predetermined fixed value.
[0066]
FIG. 5 is a diagram showing a circuit simulation device and a circuit simulation method according to the present embodiment. In FIG. 5, the device configuration and each step are the same as those in FIG. 3 except that step S307a is changed to step S307b.
[0067]
Step S307b will be described. As shown in FIG. 5, in step S307b, when the value of the relaxation factor Gramp is larger than the preset threshold value Gtran, the current value corresponding to the value of the counter k is determined in the same manner as in the first embodiment. Relaxation rate of Rate1 ^(K) Is set as the parameter Grate, and a process of subtracting the value of the parameter Grate from the current value of the relaxation factor Gramp is performed to decrease the value of the relaxation factor Gramp.
[0068]
On the other hand, when the value of the relaxation factor Gramp becomes equal to or smaller than the threshold value Gtran, that is, when the value of the virtual conductance Gmin is equal to the second predetermined value Gmin0 × 10 ^Gtran When the following occurs, ^(K) Is not set as the parameter Grate, but a preset fixed relaxation ratio Grate2 is set as the parameter Grate, and a process of subtracting the value of the parameter Grate from the current value of the relaxation factor Gramp is performed to reduce the value of the relaxation factor Gramp. . That is, in this case, the relaxation ratio Rate1 in step S301 ^(K) Do not reset the settings. Note that, of course, the second predetermined value Gmin0 × 10 ^Gtran Is set to be larger than the virtual conductance reference value Gmin0.
[0069]
Thereby, the relaxation value 10 ^Grate Is a predetermined fixed value 10 ^Rate2 Is changed, and the relaxation value after the change is 10 ^Rate2 , The value of the virtual conductance Gmin is gradually reduced. Here, the relaxation value after the change is 10 ^Rate2 Although the case where the value of the virtual conductance Gmin is gradually reduced by dividing by the above equation, the method of decreasing is not limited to the division, but may be another operation such as subtraction.
[0070]
The other points are the same as those of the circuit simulation method, the circuit simulation apparatus, and the circuit simulation program according to the first embodiment, and thus the description will be omitted.
[0071]
Specific examples of the threshold value Gtran and the fixed relaxation ratio Rate2 are as follows. That is, for example, Gtran = 4.0 and Grate2 = 1.0 may be set. These data are also set in advance by the operator of the circuit simulation and stored in the circuit information storage unit 10.
[0072]
Under these set values, the above processing is as follows, using the numerical examples used in the first embodiment as well.
[0073]
In the first embodiment, when k = 1, the value of Gramp decreases from 6.0 → 4.5 → 3.0 → 1.5 → 0.0, so Gmin ^(J) Is also 1 × 10 ^-6.0 → 1 × 10 ^-7.5 → 1 × 10 ^-9.0 → 1 × 10 ^-10.5 → 1 × 10 ^-12.0 And had decreased. However, in the present embodiment, when the value of Gramp becomes equal to or less than Gtran = 4.0, the value of Gramp is fixed to Grade2 = 1.0, and the value of Gramp is 6.0 → 4.5 → 3. 0 → 2.0 → 1.0 → 0.0 and Gmin ^(J) Is also 1 × 10 ^-6.0 → 1 × 10 ^-7.5 → 1 × 10 ^-9.0 → 1 × 10 ^-10.0 → 1 × 10 ^-11.0 → 1 × 10 ^-12.0 And will decrease.
[0074]
Similarly, in the case of k = 2, when the value of Gramp becomes equal to or less than Gtran = 4.0, the value of Grap is fixed to Grade2 = 1.0, so the value of Gramp is 6.0 → 4.4 → 2. .8 → 1.8 → 0.8 → −0.2 and Gmin ^(J) Is also 1 × 10 ^-6.0 → 1 × 10 ^-7.6 → 1 × 10 ^-9.2 → 1 × 10 ^-10.2 → 1 × 10 ^-11.2. → 1 × 10 ^-12.2. And will decrease. The same processing is performed when k = 3 or later.
[0075]
According to the present embodiment, the value of virtual conductance Gmin is the second predetermined value Gmin0 × 10 ^Gtran When the value is below, the relaxation value is 10 ^Grate Is a predetermined fixed value 10 ^Rate2 And the value Gmin of the virtual conductance is gradually reduced by performing an operation such as division by the changed relaxation value, and the solution processing is performed.
[0076]
Therefore, as in the first embodiment, the relaxation rate Rate1 ^(K) Is set to 1.5 (for k = 1) or 1.6 (for k = 2), and the relaxation value 10 ^Grate Is set to a large value, while the fixed relaxation rate Rate2 is set to 1.0, and a predetermined fixed value 10 is set. ^Rate2 If is set to a small value, the value of the virtual conductance can be significantly changed in the initial stage of the solution processing to improve the tracking efficiency of the solution, while the virtual conductance of the virtual conductance becomes closer to the true value in the final stage of the solution process. It is possible to obtain the true value with high precision by changing the value finely.
[0077]
<Embodiment 3>
This embodiment is also a modification of the circuit simulation method, the circuit simulation device, and the circuit simulation program according to the first embodiment, and in step S307a in the first embodiment, the value generated based on the random number is changed to the relaxation value. , The value of the virtual conductance is gradually reduced by dividing the relaxation value after the calculation.
[0078]
FIG. 6 is a diagram showing a circuit simulation device and a circuit simulation method according to the present embodiment. In FIG. 6, the device configuration and each step are the same as those in FIG. 3, except that step S307a is changed to step S307c.
[0079]
Step S307c will be described. As shown in FIG. 6, in this step S307c, the current mitigation rate Rate1 according to the value of the counter k ^(K) And a value obtained by adding a random number rand () to the parameter Grate, and subtracting the value of the parameter Grate from the current value of the mitigation factor Gramp to reduce the value of the mitigation factor Gramp. Note that the random number rand () may be an arbitrary value having no upper and lower limits in the generation range, but may be limited to an arbitrary value within a predetermined range such as 0 ≦ rand () ≦ 1.
[0080]
This means that each time the operation using the relaxation value is performed, in step S302, the value 10 generated based on the random number rand () is used. ^{rand ()} 10 ^{Grate1 (k)} While multiplying the relaxation value of ^{Grate1 (k) + rand ()} Divided by the virtual conductance Gmin ^(J) Means to decrease the value of.
[0081]
In the above, the value 10 generated based on the random number rand () is used. ^{rand ()} Relaxed value 10 ^{Grate1 (k)} Has been shown, but other operations such as addition, subtraction or division may be performed.
[0082]
In the above description, the relaxation value 10 after the calculation is used. ^{Grate1 (k) + rand ()} Although the case where the value of the virtual conductance Gmin is gradually reduced by dividing by the above equation, the method of decreasing is not limited to the division, but may be another operation such as subtraction.
[0083]
The other points are the same as those of the circuit simulation method, the circuit simulation apparatus, and the circuit simulation program according to the first embodiment, and thus the description will be omitted.
[0084]
According to the present embodiment, the value 10 generated based on the random number rand () ^{rand ()} Relaxed value 10 ^{Grate1 (k)} While calculating the relaxation value 10 after the calculation. ^{Grate1 (k) + rand ()} Reduces the value of the virtual conductance Gmin. Therefore, the relaxation value can be changed at random, and solvability may be increased.
[0085]
Note that, in the present embodiment, the counter k is incremented, the value of the counter k is determined in step S308, and the relaxation ratio Rate1 is determined in step S301. ^(K) May not be performed. In that case, the resetting of the relaxation value in the Gmin-Stepping method is not performed. This embodiment is characterized in that the relaxation value is randomly changed by a value generated based on a random number every time the calculation using the relaxation value is performed. Are also included in the scope of the present invention.
[0086]
<Modification>
In the first to third embodiments, the Newton method is employed as the iterative solution in steps S303 to S305. However, as mentioned in Patent Document 1 as another example of the solver, the iterative solving method includes a Damped-Newton method and a homotopy method in addition to the Newton method.
[0087]
Therefore, in the first to third embodiments, other iterative solutions such as the Damped-Newton method and the homotopy method may be employed instead of the Newton method. Then, an iterative solution suitable for the circuit to be simulated can be selected, and in this case, the same effect as above can be obtained.
[0088]
Further, in the circuit simulation apparatus described in Patent Document 1, a normal Gmin-Stepping method is cited as one of the selectable solvers, but the Gmin-described method of the present application is used instead of the normal Gmin-Stepping method. -The Stepping method may be adopted.
[0089]
【The invention's effect】
According to the first aspect of the present invention, when the solution does not converge in the iterative solution and a predetermined cutoff condition is satisfied, the relaxation value is changed and the solution calculation process is performed again. Therefore, when performing the Gmin-Stepping method, there is no need to re-enter the relaxation value, and the burden of reviewing the step-down method imposed on the circuit simulation operator is reduced. In the case where the solution processing is performed by the relaxation method, the possibility of solution may be expanded by changing the relaxation value. Therefore, according to the first aspect of the present invention, a solution can be easily obtained in the solution processing of the network equation.
[0090]
According to the fifth aspect of the present invention, the relaxation value is randomly changed by the value generated based on the random number every time the calculation using the relaxation value is performed. Therefore, the solvability may be increased.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating a part of an example of a circuit to be simulated;
FIG. 2 is a diagram illustrating a virtual resistor Gmin introduced at a predetermined position in a circuit in the Gmin-Stepping method.
FIG. 3 is a diagram showing a circuit simulation device and a circuit simulation method according to the first embodiment.
FIG. 4 is a diagram showing a detailed configuration of a circuit simulation device according to the first embodiment.
FIG. 5 is a diagram showing a circuit simulation device and a circuit simulation method according to a second embodiment.
FIG. 6 is a diagram showing a circuit simulation device and a circuit simulation method according to a third embodiment.
[Explanation of symbols]
10 circuit information storage unit, 20 circuit network equation solving unit, 30 calculation result output unit.

Claims (7)

(A) inputting a virtual conductance used to create a network equation for a circuit specified by circuit information, a relaxation value used to change the virtual conductance, and a solution of the network equation to a computer; Setting each to a predetermined initial value;
(B) creating the circuit network equation based on the circuit information while introducing a virtual resistor having the virtual conductance at a location in the circuit that satisfies a predetermined condition;
(C) performing a solution process on the circuit network equation created in the step (b) by causing the computer to perform an arithmetic process using an iterative solution until the solution converges;
(D) each time the solution converges in the step (c), the value of the virtual conductance is reduced and changed by causing the computer to calculate using the relaxation value, and Performing the steps (b) and (c) by adopting new initial values of the iterative solution;
(E) determining the converged solution as a true value when the value of the virtual conductance is equal to or less than a first predetermined value in the step (d);
In the step (c), when the solution does not converge and a predetermined cutoff condition is satisfied, the relaxation value set in the step (a) is changed and the steps (b) and thereafter are performed. Circuit simulation method. The circuit simulation method according to claim 1, wherein
In the step (d), when the value of the virtual conductance becomes equal to or less than a second predetermined value larger than the first predetermined value, the relaxed value is set to a predetermined fixed value. The circuit simulation method according to claim 1, wherein
In the circuit simulation method, in the step (d), the relaxation value is randomly changed by a value generated based on a random number each time the operation using the relaxation value is performed. The circuit simulation method according to claim 1, wherein
The circuit simulation method, wherein the iterative solution in the step (c) is any of the Newton method, the Damped-Newton method, and the homotopy method. (A) inputting a virtual conductance used to create a network equation for a circuit specified by circuit information, a relaxation value used to change the virtual conductance, and a solution of the network equation to a computer; Setting each to a predetermined initial value;
(B) creating the circuit network equation based on the circuit information while introducing a virtual resistor having the virtual conductance at a location in the circuit that satisfies a predetermined condition;
(C) performing a solution process on the circuit network equation created in the step (b) by causing the computer to perform an arithmetic process using an iterative solution until the solution converges;
(D) each time the solution converges in the step (c), the value of the virtual conductance is reduced and changed by causing the computer to calculate using the relaxation value, and Performing the steps (b) and (c) by adopting new initial values of the iterative solution;
(E) determining the converged solution as a true value when the value of the virtual conductance is equal to or less than a first predetermined value in the step (d);
In the circuit simulation method, in the step (d), the relaxation value is randomly changed by a value generated based on a random number each time the operation using the relaxation value is performed. A circuit simulation apparatus using the circuit simulation method according to claim 1, wherein:
Comprising the computer,
The computer is
A storage unit for storing the circuit information,
A circuit equation solving unit for executing steps (a) to (e) of the circuit simulation method according to any one of claims 1 to 5,
A circuit simulation apparatus including a calculation result output unit for outputting a simulation result in the circuit network equation solving unit. A circuit simulation program for causing a computer to execute steps (a) to (e) of the circuit simulation method according to claim 1.

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