Abstract:
A non-linear type digital-to-analog converter comprising a decoder, control switching circuits controlled respectively by the outputs of the decoder, and an exponential function generating circuit whose analog outputs are selectively produced by the operation of the control switching circuits. An input digital representation is converted to an analog voltage output which is exponentially related to the input.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to non-linear type digital-to-analog converters effectively employable for obtaining pitch determining voltage signals in electronic musical instruments in which, for instance, voltage-controlled oscillators are employed as tone generators, and more particularly to a non-linear type digital-to-analog converter capable of producing an exponential function output having, as its exponent, a value corresponding to a digital input signal applied thereto. 
     In general, there are many cases in which the provision of an exponential function output having, as its exponent, a value corresponding to a digital input signal is required. For instance, in an electronic musical instrument employing a voltage-controlled oscillator as its tone generator it is necessary to control the voltage-controlled oscillator by the use of such an exponential function output as described above in order to obtain pitch determining voltage signals. 
     In order to meet this requirement, a digital-to-analog converter such as shown in FIG. 1. has been proposed. In this conventional digital-to-analog converter, a binary-coded input signal ranging from the least significant digit a o  to the most significant digit a m-1  (which is keying information, for instance, m=6 in case of 61keys) is converted into an analog signal e o  by a digital-to-analog conversion circuit D/A, and the analog signal thus obtained is introduced to a voltage-controlled oscillator through an exponential amplifier A. In this operation, the output e o  is represented by e o  = M 1  (a o  × 2 o  + a 1  × 2 1  - - - - + a m-1  × 2 m-1 ), and the output E(out) of the amplifier A is represented by E(out) = M 2  (M 3  e o ). In these equations, M 1 , M 2  and M 3  are the circuit constants, and each of a o , a 1 , . . . , a m-1  is either 0 or 1. 
     However, the conventional digital-to-analog converter is accompanied by the following difficulties: 
     1. Since the accuracy of the least significant bit in the conversion circuit 1 is ±50%, the conversion error of the converter is increased in the case when the number of bits is small, although the conversion accuracy thereof may be high in the case of full scale. 
     2. The exponential function characteristic of a transistor or a diode is, in general, utilized for the exponential operation of the exponential amplifier A, and therefore not only the operational accuracy but also the operational speed thereof cannot be as high as expected. This difficulty is due to the thermal characteristics of circuit elements such as those described above and to a noise signal of the order of 10μV caused therein; that is, the difficulty is due to the fact that the operating characteristic of the amplifier, or the transistor or the diode is limited. 
     SUMMARY OF THE INVENTION 
     Accordingly, an object of this invention is to provide a non-linear type digital-to-analog converter in which all of the above-described difficulties accompanying a conventional digital-to-analog converter are overcome. 
     More specifically, an object of the invention is to provide a non-linear type digital-to-analog converter which produces an exponential function output having, as its exponent, a value corresponding to an input digital data signal applied thereto, without the use of an exponential amplifier. 
     Another object of the invention is to provide a non-linear type digital-to-analog converter having high accuracy and high operating speed. 
     A further object of the invention is to provide a non-linear type digital-to-analog converter having a low noise characteristic. 
     A still further object of the invention is to provide a non-linear type digital-to-analog converter whose output has a low distortion factor even if a large input signal is applied thereto. 
     The foregoing objects and other objects are achieved, according to this invention, by the provision of a non-linear type digital-to-analog converter for producing an exponential function output having, as its exponent, a value corresponding to an digital input signal applied thereto, comprising: 
     a. decoder means having digital inputs and individual outputs for decoding said digital input signal to an individual output signal; 
     b. exponential function generating means provided with output points whose number corresponds to the number of the individual outputs of said decoder means, for providing respectively at said output points analog outputs which are stepwisely different in value; and 
     c. control switching means comprising a plurality of control switching circuits connected respectively to said output points of said exponential function generating means and to the individual outputs of the decoder so that, in response to an enabled individual outputs produced by said decoder means, said analog outputs provided at said output points of said exponential function generating means are selectively introduced to a common output terminal. 
     The nature, utility and principle of this invention will be more clearly understood from the following detailed description and the appended claims when read in conjunction with the accompanying drawings in which like parts are designated by like numerals or characters. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
     FIG. 1 is a block diagram illustrating a conventional digital-to-analog converter for generating exponential functions; 
     FIG. 2 is a circuit diagram showing the theoretical configuration of an exponential function generating circuit employed in this invention; 
     FIG. 3 is a circuit diagram illustrating one example of a non-linear type digital-to-analog converter for generating exponential function outputs; 
     FIG. 4 is a circuit diagram illustrating a modification of the digital-to-analog converter according to the invention; and 
     FIG. 5 is a block diagram of an electronic musical instrument including a digital-to-analog converter of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     An example of an exponential function generating circuit employed in this invention is shown in FIG. 2. 
     This circuit is formed by resistors R 1 , R 2  and R L  which are connected to a constant d.c. voltage source Er (of a voltage Er) in the form of a ladder network as is shown in FIG. 2. More specifically the exponential function generating circuit is formed by the following steps: First, a series circuit of resistors R 1  having connection points n-1, n-2, . . . 3, 2 and 1 therebetween is formed, and resistors R 2  are connected to the connection points n-1, n-2, . . . 3, 2 and 1 of the series circuit of the resistors R 1 , respectively. The free end of the resistors R 2  are grounded. The free end of the resistor R 1   at one end of the series circuit is connected to the positive terminal (or connection point) n of the d.c. source Er having its negative terminal grounded. The free end of the resistor R 1  at the other end of the series circuit is connected to one end (or connection point 0) of the resistor R L  having the other end grounded. 
     Thus, the exponential function generating circuit has the connection points 0 through n, and output voltages E o  through E n  are obtained between the connection points 0 through n and the ground, respectively. 
     If the values of the resistors R 1 , R 2  and R L  employed in the exponential function generating circuit are selected so as to satisfy the equation of R 2  = R L  (1 + R L  /R 2 ), a voltage Ek at any stage, that is, between any connection point and the ground, can be represented by the following equation because En = Er. 
     
         Ek = Er (R.sub.L /R.sub.1 +R.sub.L).sup. n-k 
    
     where k is an integer from 0 through n. Thus, a sequence of voltages which increase in a stepwise monotonic manner are obtained at the respective connection points 0 - n. More specifically, the voltage at the point 1 is greater than that at the point 0, the voltage at the point 2 is greater than that at the point 1, and so on. 
     When the circuit shown in FIG. 2 is employed in one example of the invention described later, these connection points 0 - n serve as output points, the number of which is selected to equal a value obtained by raising the base of a binary coded signal or a digital input signal (the base being &#34;2&#34; in the case of binary number) to a power equal to the number (m) of bits in the binary coded signal. That is, in the case of an m bit binary number, the number of the connection points is 2 m , and the voltages Eo - En obtained respectively at the connection points are 2 m  different voltages which increase in a stepwise monotonic manner. 
     FIG. 3 shows one example of a non-linear type digital-to-analog converter according to this invention which includes a ladder-type function generating circuit as shown in FIG. 2. 
     The non-linear type digital-to-analog converter comprises: a decoder 11 operating to receive a binary coded input signal of digital data ranging from the least significant digit a o  to the most significant digit a m-1  and to produce 2 m  (n+1=2 m ) individual outputs by decoding the binary coded input signal; and a ladder-type function generating circuit 14 such as shown in FIG. 2. The individual outputs produced by the decoder 11 are applied through gate driving circuits 12-0 through 12-n to the control terminals of control switching means, that is, the gates of field-effect transistors 13-o through 13-n, respectively. The field-effect transistors are connected to the output points o through n of the function generating circuit 14, respectively, and produce outputs E(out) at their common output terminal E(out) in response to the gate input signals produced by the gate driving circuits. For instance, when the control switching means 13-n is rendered conductive, the output E(out) = Er is delivered to the output terminal E(out). 
     In the exponential function generating circuit illustrated in FIG. 2, the output E(out) is expressed by the following Equation (1): 
     
         E(out) = Er ×(R.sub.L /R.sub.1 +R.sub.L) .sup.n-(a.sbsp.m-1.sup.× 2.spsp.m-1 .sup.+ . . . a.sbsp.1.sup.× 2.spsp.1.sup.+a.sbsp.o.sup.× 2.spsp.o.sup.) (1) 
    
     If in order to simplify Equation (1), R L  /(R 1  +R L ) is made equal to K (R L  /(R 1  +R L )=K), then Equation (1) can be rewritten as in the following Equation (2): 
     
         E(out) = Er × K.sup.n-(a.sbsp.m-1.sup.× 2.spsp.m-1 .sup.+ . . . + a.sbsp.1.sup.× 2.spsp.1.sup.+a.sbsp.o .sup.× 2.spsp.o.sup.) (2) 
    
     Thus, an exponential function output having, as its exponent, a value corresponding to a digital input signal is obtained. Accordingly, it is apparent that the non-linear type digital-to-analog converter according to the invention can be employed in place of the converter D/A plus the exponential amplifier A shown in FIG. 1, so as to effectively drive the voltage-controlled oscillator in the electronic musical instrument. 
     A modification of the converter shown in FIG. 3, as illustrated in FIG. 4, is similar to that of FIG. 3 in signal transmitting characteristic but is different in that, in order to reduce the complexity in circuit configuration accompanying the increase of the number of outputs in the ladder type function generating circuit and also in the decoder, these outputs are divided into a plurality of groups (two groups in FIG. 4). 
     More specifically, the digital-to-analog converter, as shown in FIG. 4, comprises two decoders 11a and 11b, and two function generating circuits 14a and 14b. An output read through control switching means 13-0 through 13-(k-1) out of the function generating circuit 14b is applied through a buffer amplifier 15 to the function generating circuit 14a. 
     The decoder 11a operates to receive a binary coded input signal ranging from the least significant digit a o  to the i-th digit a i-1  and produce 2 i  outputs which are applied to control the control switching circuits 13-k  through 13-n&#39; through gate driving circuits (amplifiers) 12-k through 12-n&#39;, respectively. On the other hand, the decoder 11b receives a binary coded input signal ranging from the a i  -th digit to the most significant digit a m-1  to produce outputs which control the control switching circuits 13-0 through 13-(k-1) through gate driving circuits 12-0 through 12-(k-1). 
     During the operations, one output is produced by each of the decoders 11a and 11b, and therefore a control switching circuit of the function generating circuit 14a and a control switching circuit of the function generating means 14b are rendered conductive, respectively, as a result of which, an output E(out) is produced and delivered to the common output terminal E(out). 
     In the circuit shown in FIG. 4, if the values of the resistors R 1 , R 2  and R L , and r 1 , r 2  and r L  are determined so as to satisfy the following equations: 
     
         R.sub.2 = R.sub.L (1+R.sub.L /R.sub.1)), and r.sub.2 = r.sub.L (1+(r.sub.L /r.sub.1)), 
    
     the output E(out) can be expressed by the following equation (3): 
      E(out) = E r  × K 1 .sup.(k-1) - (a.sbsp.m-1 .sup.× 2.spsp.m-i-1 +a .sbsp.m-2.sup.× 2.spsp.m-i-2 .sup.. . . + a.sbsp.1.sup.× 2.spsp.o) × K.sup.(n&#39;-k+1) - (a.sbsp.i-1.sup.× 2.spsp.i-1 +a .sbsp.i-2 .sup.× 2.spsp.i-2  +  . . . + a.sbsp.o.sup.× 2.spsp.o)             (3) 
     where 
     K = R L  /(R 1  + R 2 ), 
     K 1  = r L  /(r 1  + r L ), and 
     K = K 1   2-i   
     This Equation (3) can be rewritten as in the following Equation (4): 
     E(out) = Er × K n&#39;-k+1+2 .spsp.i.sup.(k-) × K - (a.sbsp.m-1.sup.× 2.spsp.m-1 +a .sbsp.m-2.sup.× 2.spsp.m-2  +  . . . + a.sbsp.o.sup.× 2.spsp.o.sup.) (4) 
     This Equation (4) corresponds to the above Equation (2), and therefore it is apparent that the signal transmitting characteristic of the converter shown in FIG. 4 corresponds to that of the converter shown in FIG. 3. 
     A merit of the converter organized as shown in FIG. 4 is that circuit configuration per decoder and that per ladder-type function generating circuit can be simplified when compared with the converter shown in FIG. 3. 
     The following advantageous features are provided by the converter according to this invention as described above with respect to certain embodiments thereof. 
     1. Without employing an exponential amplifier, the converter according to this invention can produce an exponential function output having, as its exponent, a value corresponding to an input digital data signal. 
     2. Since a linear conversion circuit and an exponential amplifier are not employed in the converter according to the invention, high accuracy (0.1% with the minimum number of bits) and high speed operation can be obtained. 
     3. By the converter of this invention, an accurate attenuation ratio can be controlled in a digital mode, and therefore the converter can be used also as an attenuator. 
     4. Impedances viewed from the output points of the ladder type function generating circuit are equal, and accordingly variations in level will not change the absolute value of input thermal noise. Thus, the converter according to this invention has a low-noise characteristic. 
     5. The field-effect transistor employed as the control switching circuit in the converter according to the invention is operated in an on-off switching mode. Therefore, even if a large input signal is applied to the converter, the resultant output has a low distortion factor. 
     The digital-to-analog converter according to this invention can be suitably employed in a synthesizer type electronic musical instrument as shown in FIG. 5. A keyboard produces digital code signals representing key names. Other portions are known in this field by prior patents and actual models on sale.