JP3054454B2 - Frequency analyzer - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[Object of the Invention]

[0002]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a frequency analyzer for analyzing the frequency characteristics of a nonlinear circuit such as a switched capacitor circuit and a mixer circuit.

[0003]

2. Description of the Related Art For example, a switched capacitor circuit (hereinafter referred to as SCN) or a mixer circuit usually has two types of frequency inputs, and a conventional general-purpose circuit analyzer can efficiently analyze the frequency input. Can not. Also,
Since these circuits are often interested in the characteristics of the frequency domain, a dedicated circuit analyzer for analyzing the frequency characteristics has been developed.

The following literatures (1) to (4) are known as SCN-dedicated circuit analyzers, for example.

Reference (1) YPTsivides, "Analysis of
switched capacitive networks, "IEEE Trans.Circuits
and Syst., Vol. CAS-26, pp. 935-947, Nov. 1979. Reference (2) J. Vandewalle, HJ Deman and J. Rabasey, "
Time, frequency and z-domain modified nodal analysi
s of switched capacitor networks, "IEEE Trans.Circu
its and Syst., vol. CAS-28, pp. 186-190, Mar. 1981. Reference (3) J. Vlach, K. Singhal and M. Vlach, "Compute
r oriented formulation of equation and analysis of
switched-capacitor networks, "IEEE Trans.Circuits
and Syst., vol. CAS-31, pp. 753-765, Sept. 1984. Reference (4) MLLion and YLKuo, "Exact analysis o
f switched capacitorcircuits with arbitary input
s, "IEEE Trans.Circuits and Syst., vol.CAS-26, pp.213
-223, Apr. 1979. Each of these documents (1) to (4) describes an analysis method of a linear circuit composed of a capacitance, an independent / dependent voltage source, and an ideal switch. An equation is established using the node voltage and the electric charge as circuit variables so that the electric charge conservation law is satisfied in a certain closed system for each switch phase.

In reference (2), an MNA (MoMo) is used with a node voltage, a switch, and a charge of a voltage source as circuit variables.
The difiede Nodal Analysis Method) establishes an equation for each switch phase.

Reference (3) describes a group delay and sensitivity analysis method in addition to the amplitude and phase analysis. The node voltage and the branch current of the voltage source are used as circuit variables, and a modified nodal two-graph formulation is used. Formulate an equation for each switch phase.

Reference (4) describes a method of calculating a transfer function for an output response at a frequency different from the input frequency, and a noise analysis when the noise source does not change with time. A circuit equation is established using a method of obtaining the current voltage using the voltage immediately before the switching of the switch as an initial value.

All of the analyzers shown in these documents (1) to (4) handle only a circuit composed of only linear elements, and establish a circuit equation for each phase of a clock signal. It is what we want to analyze.

[0010] As a circuit analyzer of a mixer circuit, the one shown in the following document (5) is known.

Reference (5) V. Rizzoli, C. Cecchtti and
A. Lipparini, "Frequency conversionin general nonlin
ear multiport devices, "IEEE Microwave Theory Tec
h., vol. MTT-34, pp. 483-486, June. 1986. This reference (5)
In the mixer circuit, a modulation signal is often considered to be linear with respect to the output, and a periodic linear time-varying circuit is introduced in the frequency domain to analyze the signal.

[0012]

However, it is difficult to analyze a non-linear circuit in such a conventional SCN-dedicated analyzer, and to analyze the influence of the on-resistance of the switch and the finite band of the operational amplifier. It takes a long time to do it. Further, the conventional mixer circuit analyzer is not suitable for analyzing a large-scale circuit or a circuit having strong nonlinearity.

SUMMARY OF THE INVENTION The present invention has been made to solve such a conventional problem, and an object of the present invention is to provide a frequency analysis device capable of efficiently performing a frequency analysis of a nonlinear circuit or a linear circuit. It is in.

[Configuration of the Invention]

[0015]

To achieve the above object, the present invention comprises means for calculating a periodic stationary solution of a nonlinear circuit, and linearizing the nonlinear circuit around the calculated periodic stationary solution. A means for constructing a digital system to obtain a periodic time-varying transfer function of discrete time based on a periodic linear time-varying circuit, and calculating the periodic time-varying transfer function of discrete time using the digital system And a means for calculating the transfer function of the DC component and each harmonic component of the periodic linear time-varying circuit using the discrete-time periodic time-varying transfer function.

Further, a means for constructing a digital system for obtaining a periodic time-varying transfer function of a discrete time based on a periodic linear time-varying circuit of a linear circuit is provided. Means for calculating a periodic time-varying transfer function; means for calculating the transfer function of the DC component and each harmonic component of the periodic linear time-varying circuit using the discrete-time periodic time-varying transfer function; It is characterized by having.

[0017]

With the above arrangement, a periodic stationary solution of the nonlinear circuit is calculated, and the nonlinear circuit is linearized around the periodic stationary solution to obtain a periodic linear time-varying circuit. Then, a digital system for obtaining a discrete-time periodic time-varying transfer function is constructed based on this.

Thereafter, a discrete-time periodic time-varying transfer function is obtained from the system, and using this, the transfer function of the DC component of the periodic linear time-varying circuit and each harmonic component, that is,
I want frequency characteristics. Therefore, the frequency characteristics of a non-linear circuit including a MOS, a bipolar transistor, a diode, and the like can be efficiently analyzed.

Also, for a linear circuit, if a digital system is constructed using the periodic linear time-varying circuit of this circuit, frequency analysis can be performed in the same manner as the above-described nonlinear circuit.

[0020]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing a configuration of a frequency analysis device to which the present invention is applied.

As shown in the figure, the frequency analyzing apparatus includes an input unit 1, a steady state analyzing unit 2, a digital system construction unit 3, a first transfer function calculating unit 4, and a second transfer function calculating unit 5. And an output display unit 6.

The input unit 1 is provided with a circuit description, a control command, an output method, and the like of a circuit to be analyzed by a method similar to that of the general-purpose circuit analyzer SPICE introduced in the following document (6), or a display. This is input by a method such as selecting one displayed above with a cursor.

Reference (6) LNNagel, 2 "SPICE;2" A comp
uter program to simulate semiconductor circuits, "E
RL Memo ERL-M520, Univ.California, Berkeley, May 197
5. The steady state analysis means 2 is described in, for example, the following document (7),
A periodic steady solution is numerically calculated by using the time domain steady analysis method shown in (8).

Reference (7) M. Kakizaki and T. Sugawar
a, "A modified Newton method for the steady-state a
nalysis, "IEEE Trans.vol.CAD-4, No.4, pp.662-667, Oc
t.1985. Reference (8) S. Skelboe, "Computation of thepariodic
steady state response of nonlinear networks by ext
rapolation methods, "IEEE Trans.Circuits and Syst.,
vol.CAS-27, pp.161-175, Mar.1980. In this embodiment, a periodic stationary solution of the switching circuit and the mixer circuit when only a clock signal or a local oscillation signal (period T) is input is described. calculate.

The digital system construction means 3 uses a matrix data calculated at each integration step of numerical integration of a general-purpose circuit analysis program to generate a digital system for calculating a discrete-time periodic time-varying transfer function. Build on.

The first transfer function calculator 4 calculates a discrete-time periodic time-varying transfer function using the digital system constructed by the digital system constructor 3.

The second transfer function calculating section 5 linearizes around the periodic stationary solution using the discrete-time periodic time-varying transfer function obtained by the first transfer function calculating section 4, and The transfer function of the DC component and each harmonic component of the periodic linear time-varying circuit is numerically obtained.

The output display unit 6 writes the numerical value of the result to an output file (not shown) specified by the user. Alternatively, it is displayed on a display (not shown).

Next, the operation of this embodiment will be described.

The input section 1 shown in FIG. 1 is given a function f (y (t), y '(t)) of a nonlinear circuit shown in the following equation (1).

F (y (t), y ′ (t)) = v (t) + δv (t) (1) where v (t) is a periodic excitation having a period T, and δv (t) is an input signal. Show. Further, “′” (dash) shown in “y ′ (t)” on the left side indicates a time derivative for convenience of electronic filing. (The same applies to the following.)
Was assumed to have a _{y st (t + T) =} y st (t) at which such stable periodic solution y _st (t) when (t) = 0, (1 ) formula periodic solutions y _st of (t) Expand the tail around and take the primary term. Thus, a periodic linear time-varying circuit linearized around the periodic solution y _st (t) is given by the following equation (2).

A (t) x (t) + b (t) x ′ (t) = u (t) (2)

[0033]

(Equation 1)

A (t + T) = a (t), b (t + T) = b (t) The digital system construction unit 3 calculates a discrete-time periodic time-varying transfer function by the following procedure. Build a digital system. However, the parameters h _m , p, τ _m , and T used below are as shown in FIG.

First, when the input signal u (t) = ue ^jωt , the small signal response x (t) of the system shown in equation (2)
Is expressed using a time-varying transfer function H (jω, t), x (t) = H (jω, t) ue ^jωt (5) And, since the coefficient of the equation (2) is periodic, The function H (jω, t) is also periodic and can be represented by Fourier coefficients. Therefore, the following equation (6) is obtained.

[0036]

(Equation 2)

Where ω _s = 2π / T, and H _l (j
ω)

[0038]

(Equation 3)

## EQU2 ##

Here, assuming that H (jω, t) is invariant in the section of τ _m−1 <t ≦ τ _m (m = 1, 2,..., P), the following equation (6) is obtained. Is as shown in the following equation (8).

[0041]

(Equation 4)

[0042] However, K _m ^l is,

[0043]

(Equation 5)

Then, in order to calculate the discrete transfer function H (jω, τ _m ), the discrete time t
= ^NT + τ _m and input u (t) = ue ^jωt , and a digital system represented by the following equation (10) is considered.

[0045] _{a m x (nT + τ m} ) + b m x '(nT + τ m) = ue jω (nT + τ m) (10) However,

[0046]

(Equation 6)

When the differential term on the left side of the equation (10) is approximated by the backward Euler method,

[0048]

(Equation 7)

Is as follows. Note that, in this calculation, in addition to the backward Euler method, approximation may be performed by a trapezoidal method, Gear's higher-order integration method, or the like.

Since equation (11) is a linear system, it can be expressed by the following equation (12).

X (nT + τ _m ) = H (jω, τ _m ) ue ^{jω (nT + τ} m ⁾ (12) Then, by substituting equation (12) into equation (11) and using the periodicity of the transfer function, Equation (11) can be represented by a matrix shown in the following equation (13).

[0052]

(Equation 8)

Where J _m , X _m , and C _m are the following (14)
It is shown by the formula.

[0054]

(Equation 9)

In equation (13), u = 1, D _m ,
E _m the following equation (15), or (16) be determined as shown in equation, it is possible to construct a digital system as shown in FIG.

[0056] _{D m = (a m + b} m / h m) -1 (15a) E m = -b m / h m (15b) D m = (a m + 2b m / h m) -1 (16a) E _{m = - (a m -2b m} / h m) However (16b),

[0057]

(Equation 10)

Then, in the first transfer function calculating section 4 shown in FIG. 1, the discrete output H (j
ω, τ _m ) (m = 1, 2,..., P). Then, in the second transfer function calculation unit 5, a coefficient when the periodic time-varying transfer function is expanded by Fourier series, that is, a transfer function Ho (jω) of an output of the same angular frequency component as the input angular frequency,
And determine the transfer to the modulation output shifted by Eruomega _s than the input angular frequency function H _l (j [omega]) by the method shown in FIG.

The result is displayed on the output display unit 6.

As described above, in this embodiment, the steady-state solution of the nonlinear circuit is obtained by the steady-state analysis unit 2, and the nonlinear circuit is linearized around the steady-state solution to obtain a periodic linear time-varying circuit. The digital system constructing unit 3 constructs a digital system based on the periodic linear time-varying circuit, and the first and second transfer function calculating units 4 and 5 execute the periodic linear time-varying circuit based on this system. The transfer function of the DC component of the transformer circuit and each harmonic component is obtained.

Therefore, the transfer function of the switched capacitor circuit or the mixer circuit, that is, the frequency characteristic can be efficiently analyzed regardless of the nonlinearity of the circuit.

In this embodiment, the case where the circuit to be analyzed is a non-linear circuit has been described. However, the present invention is not limited to this, and can be applied to a linear circuit. In this case, since a periodic linear time-varying circuit of the circuit is given in advance, the process of linearizing the nonlinear circuit in the above-described embodiment may be omitted.

[0063]

As described above, according to the present invention, the frequency characteristics of the switched capacitor circuit and the mixer circuit can be efficiently analyzed regardless of the nonlinearity of the circuit. Therefore, a circuit including a non-linear element such as a MOS, a bipolar transistor, and a diode can be handled. In addition, since a periodic stationary solution is obtained in the time domain, there is no limitation in using a steady analysis method in the frequency domain such as a conventional one having a weak nonlinearity and a waveform close to a sine wave.

Further, since the input data of the circuit description prepared by the user is the same as that of the conventional general-purpose circuit analyzer, it does not impose a large burden on data input.

[Brief description of the drawings]

FIG. 1 is a block diagram showing the configuration of an embodiment of the present invention.

FIG. 2 is a block diagram illustrating a digital system for calculating a discrete-time periodic time-varying transfer function.

FIG. 3 is an explanatory diagram showing definitions of parameters h _m , τ _m , p, and T.

FIG. 4 shows a discrete output H (jω,
FIG. 9 is an explanatory diagram showing a method for obtaining a transfer function H _l (jω) based on τ _m ).

[Explanation of symbols]

 Reference Signs List 1 input unit 2 steady-state analysis unit 3 digital system construction unit 4 first transfer coefficient calculation unit 5 second transfer coefficient calculation unit 6 output display unit

Claims (2)

(57) [Claims] 1. A means for calculating a periodic stationary solution of a nonlinear circuit, and linearizing the nonlinear circuit around the calculated periodic stationary solution to obtain a periodic linear time-varying circuit. Means for constructing a digital system to determine the periodic time-varying transfer function, means for calculating a discrete-time periodic time-varying transfer function using the digital system, and a DC component of the periodic linear time-varying circuit. Means for calculating a transfer function of each harmonic component using the discrete-time periodic time-varying transfer function. 2. A means for constructing a digital system for obtaining a periodic time-varying transfer function of a discrete time based on a periodic linear time-varying circuit of a linear circuit, and a discrete-time circuit using the digital system. Means for calculating a periodic time-varying transfer function; means for calculating the transfer function of the DC component and each harmonic component of the periodic linear time-varying circuit using the discrete-time periodic time-varying transfer function; A frequency analysis device comprising: