CN104035745B - Logarithm loga x operating circuit and implementation method thereof - Google Patents

Abstract

The invention discloses the computing circuits of general logarithm loga x a kind of. Presently, there are logarithmic operational circuit be only realize natural logrithm function ln x circuit, lack general logarithm function loga x computing circuit. The present invention utilizes Mathematical equivalent relational implementation logarithmic function loga x operation, the operation to the natural logrithm ln x of input function is realized using the circuit that diode D1 and integrated transporting discharging U1 is constituted, the operation that natural logrithm ln a is realized using the circuit that diode D2 and integrated transporting discharging U1 is constituted realizes analog division using multiplier U2 and integrated transporting discharging U1 Operation realizes loga x logarithm operation. The invention is related to general logarithm loga x computing circuit, and truth of a matter a can be adjusted, increase the type of analog signal computing circuit, extend the operating range of analog signal, its structure is simple, and operation is accurate, and stability is good, the general logarithm operation that analog signal can be realized with it, will have wide practical use in integrated operational amplifier circuit.

Description

A kind of logarithm logaX computing circuit and its implementation

Technical field

The invention belongs to electronic circuit field, relate to a kind of analog circuit realizing general logarithm computing, be specifically related to one Plant and realize general logarithm function log based on natural logrithm lnx circuit and division circuit_aX computing.

Background technology

In electronic circuit, the application of integrated transporting discharging is mainly manifested in it can constitute various computing circuit, by introducing electricity Pressure negative feedback, makes amplifier be operated in linear zone, so realize the ratio of analogue signal, plus-minus, multiplication and division, integration, differential, logarithm and The elementary operations such as index.The logarithmic operational circuit that presently, there are only realizes natural logrithm function lnx (i.e. log_eX) circuit, Lack general logarithm function log_aThe computing circuit of x.In order to realize general logarithm function with satisfied different analogue signal computings Needing, the present invention proposes one and is capable of general logarithm function log_aThe analog operational circuit of x, truth of a matter a can be necessarily In the range of free value, it is also possible to realize log_aLogarithm operations such as (sin x).

Summary of the invention

For the deficiencies in the prior art, the invention provides one and realize general logarithm function log_aX computing circuit and Method, utilizes natural logrithm lnx circuit and division circuit to realize general logarithm function log_aX computing circuit.

The present invention adopts the following technical scheme that and realizes goal of the invention:

One is used for realizing logarithmic function log_aThe method of x computing circuit, comprises the following steps:

(1) according to mathematical relationship a, it is achieved logarithmic function log_aThe mathematical operation of x:

${\log }_{a}x=\frac{\ln x}{\ln a}---a$

(2) input voltage x, according to formula a, utilizes the circuit realiration logarithmic function that diode D1 and integrated transporting discharging U1 is constituted Lnx computing, the output voltage v of integrated transporting discharging U1 the 1st pin₁:

$v_1=-V_{T}ln\frac{x}{i_{D1}{R}_1}---b$

(3) also according to formula a, the circuit realiration logarithm lna computing that diode D2 and integrated transporting discharging U1 is constituted is utilized, logical Overregulating slide rheostat R2 and access the constant value of resistance regulation a, integrated transporting discharging U1 is at the output voltage v of its 14th pin₂:

$v_2=-V_{T}ln\frac{V}{i_{D2}{R}_2}---c$

(4) integrated transporting discharging U1 is used to constitute circuit v₂Anti-phase amplification computing, i.e. integrated transporting discharging U1 the 7th pin output voltage v₃:

$v_3=-\frac{R_4}{R_3}{v}_2=\frac{R_4}{R_3}{V}_{T}ln\frac{V}{i_{D2}{R}_2}---d$

(5) utilizing the division arithmetic circuit that U1 and multiplier are constituted, the output voltage at its 8th pin achieves division fortune Calculate v₄:

Whereini_D1R₁=1,

A kind of logarithmic function log_aThe computing circuit of x, this circuit is by integrated operational amplifier U1, multiplier U2, diode D1, diode D2 form, and integrated operational amplifier U1 realizes the conversion of signal, amplification, negative function, diode D1 and integrated fortune Calculate amplifier U1 to realize asking natural logrithm computing lnx, diode D2 and integrated operational amplifier U1 to realize nature input function x Logarithm operation function lna, multiplier U2 and operational amplifier U1 realize the division arithmetic function of two signal lnx and lna, the most in fact Existing general logarithm calculation function.

3rd pin of described integrated operational amplifier U1, the 5th pin, the 10th pin, the 12nd pin ground connection, the 4th pin connects + 15V power supply VCC, the 11st pin meets-15V power supply VEE；L pin meets the 2nd of integrated operational amplifier U1 by diode D1 Pin, connects the 9th pin of integrated operational amplifier U1 by potentiometer R5；7th pin connects integrated computation by potentiometer R4 and puts 6th pin of big device U1, connects the 1st pin of multiplier U2；8th pin connects the 3rd pin of multiplier U2；14th pin passes through two Pole pipe D2 connects the 13rd pin of integrated operational amplifier U1, is connect 6 pins of integrated operational amplifier U1 by potentiometer R3.

2nd pin of described multiplier U2, the 4th pin, the 6th pin ground connection, the 5th pin meets-15V power supply VEE, and the 8th draws Foot meets+15V power supply VCC；7th pin connects the 9th pin of integrated operational amplifier U1 by potentiometer R6.

The positive pole of described diode D1 meets input signal source x by potentiometer R1, and negative pole connects integrated operational amplifier U1's 1st pin.

The positive pole of described diode D2 connects DC power anode by adjustable sliding potentiometer, and negative pole connects integrated computation and amplifies 14th pin of device U1.

The present invention utilizes a kind of general logarithm computing circuit of natural logrithm circuit and division arithmetic circuit realiration, and leads to Overregulate percentage ratio regulation truth of a matter a of slide potentiometer, add the type of analogue signal computing circuit, extend analogue signal Operating range, its simple in construction, computing is accurate, and good stability can realize the general logarithm computing of analogue signal with it, at collection Become in discharge circuit and will have wide practical use.

Accompanying drawing explanation

Fig. 1 is the structure chart of the present invention.

Fig. 2 is the schematic diagram of the present invention.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is further described in detail.

Function y=log to be realized_aThe computing of x, according to mathematical relationship

$y={\log }_{a}x=\frac{\ln x}{\ln a}---a$

As long as realizingComputing.As it is shown in figure 1, the circuit utilizing diode D1 and integrated transporting discharging U1 to constitute is real The computing of existing lnx；Utilize the computing of the circuit realiration lna of diode D2 and integrated transporting discharging U1 composition；Utilize multiplier U2 and collection Amplifier U1 is become to constitute division circuit, it is achievedComputing, i.e. realizes log_aX logarithm operation.

As in figure 2 it is shown, the electric current of diode D1 and voltage:

$i_{D1}=I_S{e}^{v_{D1}/V_T},v_{D1}=V_{T}ln\frac{I_S}{i_{D1}}=V_{T}ln\frac{x}{i_{D1}{R}_1}---b$

The output voltage of integrated transporting discharging U1 pin 1:

$v_1=-v_{D1}=-V_{T}ln\frac{I_S}{i_{D1}}=-V_{T}ln\frac{x}{i_{D1}{R}_1}---c$

Same, the electric current of diode D2 and voltage:

$i_{D2}=I_S{e}^{v_{D2}/V_T},v_{D2}=V_{T}ln\frac{I_S}{i_{D2}}=V_{T}ln\frac{V}{i_{D2}{R}_2}---d$

The output voltage of integrated transporting discharging U1 pin 14:

$v_2=-v_{D2}=-V_{T}ln\frac{I_S}{i_{D2}}=-V_{T}ln\frac{V}{i_{D2}{R}_2}---e$

This voltage, after the inverting amplifier that R3, R4 and the 5th pin, the 6th pin and the 7th pin are constituted amplifies, draws the 7th The output voltage of foot is:

$v_3=\frac{R_4}{R_3}{V}_{T}ln\frac{V}{i_{D2}{R}_2}---f$

The output of the 8th pin of this input voltage and integrated transporting discharging U1 is added in the 1st pin and the 3rd pin of multiplier U2, Divider is collectively constituted, it is achieved division arithmetic, at integrated transporting discharging with the 8th pin of integrated transporting discharging, the 9th pin, the 10th pin 8th pin output voltage:

$v_4=-\frac{R_5}{R_6}\frac{v_1}{v_3}=\frac{R_5}{R_6}\frac{R_3}{R_4}\frac{ln\frac{x}{i_{D1}{R}_1}}{ln\frac{V}{i_{D2}{R}_2}}=\frac{\ln x}{\ln a}={\log }_{a}x---g$

Take at thisi_D1R₁=1,I.e. there is v₄=log_a x。

Described a kind of logarithmic function log_aThe computing circuit of x, by integrated operational amplifier U1, multiplier U2, diode D1, diode D2 form, and integrated operational amplifier U1 realizes the conversion of signal, amplification, negative function, diode D1 and integrated fortune Calculate amplifier U1 to realize asking natural logrithm computing lnx, diode D2 and integrated operational amplifier U1 to realize nature input function x Logarithm operation function lna, multiplier U2 and operational amplifier U1 realize the division arithmetic function of two signal lnx and lna, the most in fact Existing logarithmic function calculation function.

3rd pin of described integrated operational amplifier U1, the 5th pin, the 10th pin, the 12nd pin ground connection, the 4th pin connects + 15V power supply VCC, the 11st pin meets-15V power supply VEE；L pin meets the 2nd of integrated operational amplifier U1 by diode D1 Pin, connects the 9th pin of integrated operational amplifier U1 by potentiometer R5；7th pin connects integrated computation by potentiometer R4 and puts 6th pin of big device U1, connects the 1st pin of multiplier U2；8th pin connects the 3rd pin of multiplier U2；14th pin passes through two Pole pipe D2 connects the 13rd pin of integrated operational amplifier U1, is connect 6 pins of integrated operational amplifier U1 by potentiometer R3.

2nd pin of described multiplier U2, the 4th pin, the 6th pin ground connection, the 5th pin meets-15V power supply VEE, and the 8th draws Foot meets+15V power supply VCC；7th pin connects the 9th pin of integrated operational amplifier U1 by potentiometer R6.

The positive pole of described diode D1 meets input signal source x by potentiometer R1, and negative pole connects integrated operational amplifier U1's 1st pin.

The positive pole of described diode D2 connects DC power anode by adjustable sliding potentiometer, and negative pole connects integrated computation and amplifies 14th pin of device U1.

Present invention achieves a kind of general logarithm computing circuit, add the type of analogue signal computing circuit, extend The operating range of analogue signal, its simple in construction, computing is accurate, and good stability can realize the general logarithm of analogue signal with it Computing, will have wide practical use in integrated operational amplifier circuit.

Certainly, described above not restriction to invention, the present invention is also not limited to the example above, the art general Change that logical technical staff is made in the essential scope of the present invention, retrofit, add or replace, such as log_a(sin x) etc. are right Number computing falls within protection scope of the present invention.

Claims (2)

1. a logarithmic function log_aThe computing circuit of x, including integrated operational amplifier U1, multiplier U2, diode D1, two poles Pipe D2, it is characterised in that: the 3rd pin of described integrated operational amplifier U1, the 5th pin, the 10th pin, the 12nd pin ground connection, 4th pin meets+15V power supply VCC, and the 11st pin meets-15V power supply VEE；L pin connects integrated computation by diode D1 and amplifies 2nd pin of device U1, connects the 9th pin of integrated operational amplifier U1 by potentiometer R5；7th pin connects collection by potentiometer R4 Become the 6th pin of operational amplifier U1, connect the 1st pin of multiplier U2；8th pin connects the 3rd pin of multiplier U2；14th draws Foot connects the 13rd pin of integrated operational amplifier U1 by diode D2, is connect the 6 of integrated operational amplifier U1 by potentiometer R3 Pin；

2nd pin of described multiplier U2, the 4th pin, the 6th pin ground connection, the 5th pin meets-15V power supply VEE, and the 8th pin connects+ 15V power supply VCC；7th pin connects the 9th pin of integrated operational amplifier U1 by potentiometer R6；

The positive pole of described diode D1 meets input signal source x by potentiometer R1, and what negative pole met integrated operational amplifier U1 the 1st draws Foot；The positive pole of described diode D2 connects DC power anode by adjustable sliding potentiometer, and negative pole meets integrated operational amplifier U1 The 14th pin.

2. utilize circuit realiration logarithmic function log described in claim 1_aThe method of x computing, comprises the following steps:

(1) according to mathematical relationship a, it is achieved logarithmic function log_aThe mathematical operation of x:

${\log }_{a}x=\frac{\ln x}{\ln a}---a;$

(2) input voltage x, according to formula a, utilizes the circuit realiration logarithmic function ln x that diode D1 and integrated transporting discharging U1 is constituted Computing, the output voltage v of integrated transporting discharging U1 the 1st pin₁:

$v_1=-V_T\ln \frac{x}{i_{D1}{R}_1}---b;$

Wherein i_D1Electric current for diode D1；

(3) also according to formula a, the circuit realiration logarithm lna computing that diode D2 and integrated transporting discharging U1 is constituted is utilized, by adjusting Joint slide rheostat R2 accesses the constant value of resistance regulation truth of a matter a, and integrated transporting discharging U1 is at the output voltage v of its 14th pin₂:

$v_2=-V_{T}ln\frac{V}{i_{D2}{R}_2}---c;$

Wherein i_D2Electric current for diode D2；

(4) integrated transporting discharging U1 is used to constitute circuit v₂Anti-phase amplification computing, i.e. integrated transporting discharging U1 the 7th pin output voltage v₃:

$v_3=-\frac{R_4}{R_3}{v}_2=\frac{R_4}{R_3}{V}_{T}ln\frac{V}{i_{D2}{R}_2}---d;$

(5) utilizing the division arithmetic circuit that integrated transporting discharging U1 and multiplier are constituted, the output voltage at its 8th pin achieves and removes Method computing v₄:

$v_4=-\frac{R_5}{R_6}\frac{v_1}{v_3}=\frac{R_5}{R_6}\frac{R_3}{R_4}\frac{ln\frac{x}{i_{D1}{R}_1}}{ln\frac{V}{i_{D2}{R}_2}}=\frac{\ln x}{\ln a}={\log }_{a}x---e;$

Wherein