Logarithmic intermediate-frequency amplifier

Abstract: A C-MOS logarithmic IF amplifier is provided which comprises a plurality of IF amplifiers cascade-connected to each other through a first coupling capacitor, a plurality of rectifiers each receiving a signal from the corresponding one of the plurality of IF amplifiers through a second coupling capacitor different in capacity from the first coupling capacitor, and an adder for adding the output signals of these rectifiers to each other. The first and second coupling capacitors are preferable to be connected in series to cascade-connect those IF amplifiers therethrough. Each of the rectifiers is applied with an output signal of the corresponding one of the IF amplifier from the connection point of the corresponding first and second coupling capacitors. By setting the first and second capacitors at optimum capacitive values, respectively, the IF amplifiers each makes it possible to cut off the low band side of its frequency band and the rectifiers each makes it possible to expand its frequency band to the low band side.

Description: This invention relates to a logarithmic intermediate-frequency amplifier, and more particularly, to a logarithmic intermediate-frequency amplifier having true logarithmic characteristic. In general, a logarithmic intermediate-frequency (IF) amplifier comprises IF amplifiers cascade-connected to each other in a multistage connection manner, rectifiers for receiving output signals of these IF amplifiers in a successive manner, and an adder for adding all output signals of these rectifiers to each other, and is generally formed on a bipolar integrated circuit. This is based on such advantageous facts that a bipolar transistor is superior in noise characteristic as well as small in sensitivity degradation when considered from the viewpoint of a received input, and it can be driven even at a low impedance or at a large capacity because the bipolar transistor has a high drivability and the like. In the prior-art document JP-A-62-293808, the combination of two common-source FETs at each stage serves as an IF amplifier. The common-source FETs located at adjoining two stages are cascaded through a capacitor. Each of the common-source FETs has another FET for monitoring a drain current of the common-source FET. The monitoring FET is connected in parallel to the corresponding common-source FETs. The monitored drain currents of the common-source FETs located at the first to n-th stages are added to one another by an adder circuit to thereby realize a logarithmic amplifier. EP-A-484 139 (document under Port 54(3)EPC) also discloses a logarithmic amplifier. Recently, a C-MOS logarithmic IF amplifier has been demanded to be developed in order to effectively use the advantages of the C-MOS integrated circuit. In this case, however, the following problems have been pointed out on a structural basis; An MOS transistor is large in 1/f noise, so that it is required to have an intermediate-frequency (IF) band cut off its low band side in order to prevent the sensitivity from being degraded from the viewpoint of a received input. A so-called HPF (High Pass Filter) characteristic to cut off this low baad side can be equivaiently obtained by providing IF amplifiers in a multistage cascade-connection manner through coupling capacitors. In this case, however, a coupling capacitor to be inserted is desired to be small in capacity. On the other hand, the multistage connection of the IF amplifiers through the coupling capacitors makes that the rectifiers receiving output signals of respective IF amplifiers differentiate the signal waveforms thereof, thus making it easy to vary the direct-current value of an output of each rectifier. As a result, in order to obtain a good linear logarithmic characteristic, it is unavoidably required to expand the frequency band of an input signal of each rectifier to the low frequency side, that is, it is required that the capacity of a coupling capacitor to be insertedly used be increased. Accordingly, in order to practically realize the C-MOS logarithmic IF amplifier, such a problem has been arisen that for the capacity of a coupling capacitor to be used, such contradictory requirements as shown above must be satisfied. In addition, in case that the capacity of a coupling capacitor to be used is increased, there arises a problem with on the drivability of the IF amplifier itself as well. Next, as a pseudo - logarithmic IF amplifier of a polygonal line approximation type formed on a C-MOS integrated circuit, such a circuit as is, for example, shown in Fig. 1 is known conventionally. This circuit is disclosed in the JP-A-62-292010, and comprises n differential amplifiers respectively including MOS transistor pairs (T01, T01), (T02, T02) ..., and (T0n, T0n) and constant-current sources I01, I02, ..., and I0n. These differential amplifiers are cascaded in a n-stage connection manner. The differential amplifiers of the first through nth stages are connected to full-wave rectifiers comprising two pairs of transistors (T11 and T1k), (T21 and T2k), ..., and (Tnl and Tnk), and n constant-current sources I11, I12, ..., and I1n for driving these two pairs of transistors, respectively. The differential amplifier of the (n+1)th stage has a full-wave rectifier comprising two pairs of MOS transistors ( T(n+1), and T(n+1)k) and two constant-current sources In(n+1) for driving the two pairs of them. and receiving an output signal of the differential amplifier at the nth stage. These 2(n+1) pairs of transistors (T11 and Tlk), (T21 and T2k), ..., and (T(n+1)1 and T(n+1)k) forming full-wave rectifiers each have a gate-width (W) and gate-length (L) ratio (W/L) of 1:k (k>I) thereby to constitute an unbalanced differential pair. Then, in respective two pairs, the transistors having a gate-width (W) and gate-length (L) ratio (W/L) of one (1), or (T11 and T11), (T21 and T21), ·····, and (T(n+1)I and T(n+1)I) have the drains and gates connected respectively in common, and on the other hand, those having the ratio (W/L) of k. or the transistors (T1k and T1k), (T2k and T2k), ···, and (T(n+1)k and T(n+1)k) have the drains and gates connected respectively in common. Next to the (n+1)th stage, an adder comprising three MOS transistor pairs (T10, T20), (T30, T40) and (T50, T60) is provided, which sums up the outputs of the full-wave rectifiers of the first to the (n+1)th stages. For the pseudo-logarithmic IF amplifier arranged as above, the operation will be described below. First, a transconductance parameter a can be expressed in terms of the gate-width and gate-length ratio (W11/L11) of the transistor T11 at the first stage by the following equation (1); α = µn(Cox/2) (W1/L1) where, µn is a mobility of the MOS transistor; and Cox is a gate oxide film capacity per unit area. In addition, with the transistor pair (T11, T1k) at the first stage, a ratio k between the gate-width and gate-length ratio of one transistor Tli of the pair and that of the other transistor Tlk can be expressed as follows; k= (W1k/L1k) (W11/L11) Further in addition, in the two pairs of transistors (T11 and T1k) of the first stage, if the gate-to-source voltages of respective transistors are expressed as Vgs1, Vgs2, Vgs3 and Vgs4, and the threshold voltage of each transistor is expressed as Vt, the currents I1, I2, I3 and I4 of respective transistors can be expressed as follows; I1 = α (Vgs1 - Vt) 2 I2 = k α (Vgs2 - Vt) 2 I3 = α (Vgs3 - Vt) 2 I4 = k α (Vgs4 - Vt) 2 Here, these currents I1, 12, I3 and I4 can be expressed in terms of a current I11 of the constant-current source of the first stage as follows; I1 + I2 = I11 I3 + I4 = I11 Also, an input voltage VIN of the two pairs of transistors (T11 and T1k) of the first stage can be expressed in terms of the gate-to-source voltages Vgs1, Vgs2, Vgs3 and Vgs4 of the transistors as follows; VIN = Vgs1 - Vgs2 = Vgs4 - Vgs3 As a result, an output current ΔI1 of the two pairs of transistors (T11 and T1k) can be expressed as follows: ΔI1 = (I1 - I2) - (I4 - I3) = -2(1 - 1/k) {(1 + 1/k)·I11 - 2α·VIN 2 } (1 + 1/ k) 2 From Eq.(10), it can be found that the output current ΔI1 has a square full-wave rectification characteristic with respect to the input voltage VIN. In the same manner as above, an output current ΔI2 of the two pairs of transistors (T21 and T2k) of the second stage ·····, and an output current In+1 of the two pairs of the transistors (T(n+1)1 and T(n+1)k) can be respectively expressed as follows; Here, it is clear that the output currents ΔI1, ΔI2 ···, ΔIn+1 and the constant-current sources I11, I22, ···, and In(n+1) of respective stages are related as shown by the following equations (13) to (15); -2I11 ≦ ΔI1 ≦ 2I11 -2I22 ≦ ΔI2 ≦ 2I22 This means that even if the input voltage VIN and the output voltages V1, V2 ····, VOUT of respective stages are made large, the output currents ΔI1, ΔI2···, ΔIn+1 are always within the respective ranges shown by Eqs.(13) to (15). In addition, the voltages V1, V2, ..., VOUT are output voltages of the differential amplifiers of respective stages, and as the input voltage VIN is increased gradually, these voltages are successively saturated in the order of VOUT, ····V2, and V1. Also, the output current IOUT of the adder consisting of the three MOS transistor pairs (T10, T20), (T30, T40) and (T50, T60) can be expressed as follows; IOUT = ΔI1 + ΔI2 + ... + ΔIn+1 As a result, by suitably setting the constant current values I01, I02, ···, and I0n of the constant-current sources of respective stages and the resistance values R01, R02, ···, and R0n of resistors to be connected to the drains of respective transistors, the maximum output voltages of the differential amplifiers of respective stages can be made of a constant sign. This means that the characteristic of the output current IOUT can be made approximately of a logarithmic characteristic to the input voltage VIN. With the conventional pseudo-logarithmic IF amplifier arranged as shown above, one full-wave rectifier consists of two unbalanced differential transistor pairs and as a result, the constant-current sources is required to be used twice in number as the rectifiers, resulting in the problem that current consumption unavoidably becomes large. In addition, considering from the viewpoint of the circuit structure, one rectifier uses two unbalanced differential transistor pairs and as a result, the circuit scale disadvantageously becomes large. This invention was made with a view to solving the above-mentioned problems, an object of is invention being to provide a logarithmic IF amplifier in which contradictory requirements on the capacity of a coupling capacitor to be inserted can be satisfied thereby to be formed on a C-MOS integrated circuit. The above object is solved with the features of the claims. Each rectifier is applied with an output signal of the corresponding one of the IF amplifiers at the connection point of the corresponding first and second coupling capacitors. An IF amplifier to be used for this invention is not specifically limited in structure thereby, an arbitrarily structured one can be used therefor, and a rectifier to be used for this invention is not specifically limited in structure thereby, so that either of a half-wave or full-wave rectifier can be used therefor. With the C-MOS logarithmic IF amplifier of this aspect, the IF amplifiers are connected through the first coupling capacitor to each other and the rectifiers are connected to each other through the second coupling capacitor different in capacity from the first coupling capacitor. As a result, by setting the first and second coupling capacitors at optimum capacitive values respectively, the IF amplifiers each make it possible to have their frequency bands cut off on the low band side thereof, and the rectifiers each make it possible to have their frequency bands expanded to the low band side. Accordingly, 1/f noise of an IF amplifier can be reduced thereby restricting degradation of noise figure (NF). In addition, the input band of a rectifier can be expanded to the low band side thereby obviating excessive signal differentiation and positively maintaining linearity of the logarithmic characteristic. Consequently, the C-MOS logarithmic IF amplifier according to this invention can be realized on a C-MOS integrated circuit. Fig. 1 is a circuit diagram showing an example of a conventional pseudo-logarithmic IF amplifier. Fig. 2 is a circuit block diagram of a C-MOS logarithmic IF amplifier according to a first embodiment of this invention. Fig. 3 is a circuit block diagram of a C-MOS logarithmic IF amplifier according to a second embodiment of this invention. Fig. 4 is a circuit diagram showing one example of a rectifier to be used in the amplifier shown in Fig. 2 or 3. Fig. 5 is a circuit diagram showing another example of a rectifier to be used in the amplifier shown in Fig. 2 or 3. The preferred embodiments of this invention will be described below while referring to Figs. 2 to 5. Fig. 2 shows a C-MOS logarithmic IF amplifier according to a first embodiment of this invention, in which a plurality of IF amplifiers A1, A2, ··· are cascaded in a multistage connection manner in order to amplify an IF signal successively. The multistage cascade - connected amplifiers A1, A2,··· have rectifiers B1, B2,··· connected thereto in order to rectify their output signals, respectively. Output signals of the rectifiers B1, B2, ··· are sent to an adder C to be added to each other and outputted. The IF amplifiers A1, A2, ··· the rectifiers B1, B2,··· and the adder C are respectively made of MOS transistors. These IF amplifiers A1, A2, ··· are cascade-connected to each other through two capacitors which are connected in series between each adjacent two of these IF amplifiers. Each of the IF amplifiers A1, A2,··· is connected to the corresponding one of these rectifiers B1, B2, ··· at the connection point of the two capacitors connected in series therebetween. Namely, the IF amplifiers A1 and A2 are cascade-connected to each other through the capacitors CA1 and CB1 which are disposed in series therebetween. The IF amplifier A1 is connected to the rectifier B1 at the connection point of the capacitors CA1 and CB1. In addition. the IF amplifiers A2 and A3 are cascade-connected to each other through the capacitors CA2 and CB2 which are disposed in series therebetween, and the IF amplifier A2 is connected to the rectifier B2 at the connection point of the capacitors CA2 and CB2. The IF amplifiers A3 and A4, A4 and A5,··· are cascade-connected to each other and connected correspondingly to the rectifiers B3, B4,··· in the same manner as shown above. In the following description, an IF amplifier Ai, rectifier Bi and capacitors CAi and CBi (i = 1. 2,···) represent typical amplifiers, rectifiers and capacitors, respectively. Thus, an input signal to a rectifier Bi is supplied to the gate of a MOS transistor thereof, so that the input impedance becomes high and yet the direct-current biasing to the gate can be made of a high input impedance. As a result, if the input impedance of the rectifier Bi is neglected. a combined capacity Ci of the capacitors CAi and CBi can be approximated as follows; Ci ≒ (CAi CBi)/(CAi+CBi) That is, the IF amplifiers Ai and A(i+1) are coupled through the combined capacity Ci to each other, and the IF amplifier Ai and the rectifier Bi are coupled to each other through only the capacity of the capacitor CAi. In addition, the low band side of a frequency band is determined by the differential characteristic ( HPF characteristic) of each coupling capacitor. As a result, the ratio of a low band side cut-off frequency fcIFi of the IF amplifier Ai and a low band side cut-off frequency fcRECTi of the rectifier Bi can be expressed as follows: fcIFi/fcRECTi ≒ CAi/Ci = (CAi/CBi) + 1 (>1) From Eq.(22), it can be found that the low band side cut-off frequency fcIFi of the IF amplifier Ai can be made high compared with the low band side cut-off frequency fcRECTi of the rectifier Bi. In this case. a load capacity of the IF amplifier Ai is the combined capacity Ci, however, if CAi = CBi = Co. from Eq.(21), Ci = (1/2) Co. which means that the capacity of an inter-stage coupling capacitor of the IF amplifier Ai becomes half that of a coupling capacitor with the rectifier Bi. As a result, from Eq.(22), fcIFi = 2fcRECTi is obtained, which means that the low band side cut-off frequency of the rectifier Bi can be decreased up to a half of that of the IF amplifier Ai. Consequently, according to this invention, an IF amplifier is allowed the low band side of its frequency band to be cut off and on the other hand, a rectifier is allowed its frequency band to be expanded to the low band side, so that a logarithmic IF amplifier can be obtained which is formed on a C-MOS integrated circuit without any important problem. Fig. 3 shows a C-MOS logarithmic IF amplifier according to a second embodiment of this invention. In Fig. 3, an IF amplifier Ai is connected through a capacitor CBi to an IF amplifier A(i+1) and through a capacitor CAi whose capacity is different from that of the capacitor CBi to a rectifier Bi. Other components are arranged as explained in the first embodiment. The C-MOS logarithmic IF amplifier of this embodiment makes it possible to obtain the same effects as shown in the first embodiment. First Example of Rectifier to be used in First and Second Embodiments: In the first and second embodiments, any circuit made of C-MOS transistor can be arbitrarily used as the rectifier Bi. In this case. however, a squaring circuit can be pointed out as an example as shown in Fig. 4, which is disclosed in JP-A-63-24377, thus being used as a squaring full-wave rectifier. In Fig. 4, the squaring circuit comprises a first differential transistor-pair consisting of a MOS transistor T1 with a gate-width and gate-length ratio (W1/L1) and a MOS transistor T2 with a gate-width and gate-length ratio (W2/L2) and a second differential transistor-pair consisting of a MOS transistor T3 with the same ratio as that of the transistor T1, (W1/L1), and a MOS transistor T4 with the same ratio as that of the transistor T2, (W2/L2). In this case, if the ratio (W1/L1) is made one (1), the ratio (W2/L2) is made k. The transistors T1 and T2 have the sources connected in common and the transistors T3 and T4 have the sources connected in common, which are connected through their connection points to constant-current sources I0, respectively. The gate of the transistor T1 is connected to that of the transistor T4, and the gate of the transistor T2 is connected to that of the transistor T3. The collector of the transistor T1 is connected to that of the transistor T3, and the collector of the transistor T2 is connected to that of the transistor T4. An input voltage VIN is applied across the common gate of the transistors T1 and T4 and the common gate of the transistors T2 and T3, which are different in the gate-width and gate-length ratio from each other. Transistors T5 and T6 each is the primary side transistor of a current mirror circuit. A subtracting circuit S subtracts a current flowing in the output line of the second differential pair from a current flowing in the output line of the first differential pair. VDD is a voltage source. With the circuit arranged as above, the characteristics will be explained below. Drain currents Idl and Id2 of the transistors T1 and T2 of the first differential pair and drain currents Id3 and Id4 of the transistors T3 and T4 of the second differential pair can be expressed as follows; Id1 = α1(VGS1 - VT) 2 Id2 = α 1·k(VGS2 - VT) 2 Id3 = α 1(VGS3 - VT) 2 Id4 = α 1·k1(VGS4 - VT) 2 where, VGS1, VGS2, VGS3 and VGS4 are gate-to-source voltages of the transistors T1, T2, T3 and T4, respectively, and VT is the threshold voltage of each transistor. In these equations, if the mobility of an electron of MOS traasistor is expressed as µn and the gate oxide film capacity per unit area of MOS transistor is expressed as Cox, the following equations can be obtained, as α1 = µn(Cox/2) (W1/L1) k1 = (W2/L2)/(W1/L1) In addition. the constant-current value I0 of the constant-current source, and the input voltage VIN can be expressed as follows; Id1 + Id2 = I0 Id3 + Id4 = I0 VGS1 - VGS2 = VIN VGS3 - VGS4 = VIN Here, if ΔIdI is defined as ΔIdI = Id1 - Id2 it can be obtained by the following equation, as ΔIdI = [-(1+1/k1) (1-1/k1)I0 + 2α1·(1+1/K1)·VIN 2 + 4α1·VIN·(1/K1 1/2 )·{(1+1/K1)(I0/α1)-VIN 2 )} 1/2 ]/(1+1/k1) 2 In addition, if ΔIdII is defined as ΔIdII = Id3 - Id4 it can be obtained as follows; ΔIdII = [(1+1/k1) (1-1/k1)I0 + 2α1·(1-1/K1)VIN 2 + 4α1·VIN (1/K1 1/2 ){(1+1/K1)(I0/α1)-VIN 2 )} 1/2 ]/(1+1/k1) 2 Hence, ΔId = ΔIdI - ΔIdII = [-2(1+1/k1) (1-1/k1)I0 + 4α1·(1-1/K1)VIN 2 ]/(1+1/k1) 2 From Eq.(37), it can be found that the current difference ΔId includes the square term of the input voltage VIN. On the other hand, the current difference Δ Id can be expressed as follows; ΔId = (Id1 + Id3) - (Id2 + Id4) From Eq.(38), it can be found that such an output current that is expressed by Eq.(37) including the square term of the input voltage VIN can be obtained by the subtracting circuit S. As explained above, the square characteristic can be obtained with a simple circuit arranged as shown in Fig. 4, which comprises two differential pairs each consisting of two transistors different in the gate-width and gate-length ratio (W/L) from each other, and in which the transistors with the same gate-width and gate-length ratio (W/L) have the drains connected in common to each other and yet, their outputs become opposite in phase. Second Example of Rectifier to be used in First and Second Embodiments : Another example of a squaring 'circuit to be used in these embodiments is shown in Fig. 5, which comprises four MOS transistors. In Fig. 5, MOS transistors M1 and M2 constitute a first differential transistor-pair to be driven by a constant-current source I0, and MOS transistors M3 and M4 constitute a second differential transistor-pair to be driven by a constant-current source obtained as follows : {2·k2 1/2 /(k2+1)}·I0 Further in Fig. 5, the drain of the transistor M1 is connected to that of the transistor M3, and the drain of the transistor M2 is connected to that of the transistor M4. The gate of the transistor M1 is connected to that of the transistor M4, and the gate of the transistor M2 is connected to that of the transistor M3. Here, with the first differential pair, if the gate-width (W1) and gate-length (L1) ratio (W1/L1) of the transistor M1 is made one (1), the gate-width (W2) and gate-length (L2) ratio (W2/L2) of the transistor M2 is k2. That is, Eq.(28) can be satisfied between them. Referring to the second differential pair, the gate-width (W3) and gate-length (L3) ratio (W3/L3) of the transistor M3 is equal to the gate-width (W4) and gate-length (L4) ratio (W4/L4) of the transistor M4, which can be expressed in terms of k2 as follows: (W3/L3) = (W4/L4) = {4k2·k2 1/2 /(k2+1)} 2 As a result, the drain currents Id1' and Id2' of the transistors M1 and M2 of the first differential pair can be respectively expressed as follows; where VGS1'and VGS2' show the gate-to-source voltage of the transistors M1 and M2 respectively. Id1' = µn(Cox/2) (W1/L1) (VGS1'-VT) 2 Id2' = µn(Cox/2) k(W1/L1) (VGS2'-VT) 2 In addition, the constant-current I0 and the input voltage VIN can be respectively obtained as follows; Id1' + Id2' = I0 VGS1' - VGS2' = VIN Here, if the difference of the Id1' and Id2' is expressed as IdP, or ΔIdP = Id1' - Id2' it can be obtained as follows; ΔIdP = -(1-1/k2)·{(1+1/k2)I0-2α2·VIN 2 } + 4α2{(1+1/K2)(I0/α2)-VIN 2 } 1/2 (1+1/k2) 2 Similarly, the drain currents Id3' and Id4' of the transistors M3 and M4 can be respectively expressed as follows; Id3' = {4k2· k2 1/2 /(k2 + 1) 2 }·α2(VGS3' - VT) 2 Id4' = {4k2· k2 1/2 /(k+1) 2 }·α2(VGS4'- VT) 2 In addition, the constant-current and the input voltage can be respectively expressed as follows; Id3' + Id4' = {2·k2 1/2 /(k2 + 1)}·I0 VGS4' - VGS3' = VIN Here, if the difference of the Id3' and Id4' is expressed as IdQ, or ΔIdQ = Id3' - Id4' it can be obtained as follows; ΔIdQ = {-4·k2 1/2 /(2k + 1) 2 }α2·VIN × [{4·k2 1/2 ·I0/(k2+1)}·{(k2+1) 2 /4k2·k2 1/2 ·α2} - VIN 2 ] 1/2 = -{4α2·(1/k2 1/2) /(k2+1) 2 }·VIN × [{4·k2 1/2 ·I0/(k2+1)}·{(k2+1) 2 /4k2·k2 1/2 ·α2} - VIN 2 ] 1/2 As a result, the differential output current I can be obtain ed as follows; ΔI = I1 - I2 = IdP - IdQ = (1-1/k2)·{2α2·VIN 2 - (1+1/k2)·I0} (1 - 1/k2) 2 = {2k2(k2-1)α2/(k2+1) 2 }·VIN 2 - {(k2-1)/(k2+1)}·I0 From Eq.(53), it can be found that such a differential output current ΔI that is proportional to the square of the input voltage VIN can be obtained. As explained above, the squaring circuit comprises two differential pairs each consisting of two transistors whose gate-width and gate-length ratios are optimized thereby making a differential input, so that the squaring circuit is not dependent on variation in threshold voltage due to the forming dispersion of transistors.

Claims: A C-MOS logarithmic intermediate - frequency amplifier comprising: a plurality of intermediate - frequency amplifiers (A1...A5) cascade-connected through a first coupling capacitor (C B1 ...C B4 ) to each other; a plurality of rectifiers (B1...B5) each receiving a signal from the corresponding one of said plurality of intermediate-frequency amplifiers (A1...A5) through a second coupling capacitor (C A1 ...C A5 ) different in capacity from said first coupling capacitor; and an adder (C) for adding output signals of said plurality of rectifiers (B1...B5) to each other. A C-MOS logarithmic intermediate-frequency amplifier as claimed in claim 1, wherein said first and second capacitors (C B1 ...C B4 , C A1 ...C A5 ) are connected in series and said plurality of intermediate-frequency amplifiers (A1...A5) are cascade-connected through said first and second capacitors thus connected in series.

Inventors: KIMURA KATSUJI, KIMURA, KATSUJI, KIMURA, KATSUJI C/O NEC CORPORATION
Applicants: NIPPON ELECTRIC CO, NEC CORPORATION
Application year: 1992
Main classification: H03G7
IPC codes: H03G7