FR2680926A1 - Device for reducing the distortion introduced by a sample-and-hold circuit, and analog/digital converter using such a device - Google Patents

Abstract

This device essentially comprises means (102, 300) for feeding back the output of this sample-and-hold circuit, onto the input of this sample-and-hold circuit.

Description

Device for reducing distortions introduced by a sampler-blocker, and analog-digital converter including a sampler-blocker provided with such a device for reducing distortions.

 The present invention is in the field of analog signal processing.

 The object of the present invention is more particularly to reduce the distortions introduced during the processing of such signals by a system called sampler-blocker, used in particular for the conversion of an analog signal into a digital signal.

 The subject of the present invention is a device for reducing the distortions introduced by a blocker sampler, essent - llement characterized in that it comprises means for feedback of the output of this blocker sampler, on the input of this sampler-blocker.

Other objects and characteristics of the present invention will appear on reading the following description of exemplary embodiments, made in relation to the attached drawings, in which
- Figures 1, 2, 3, 4 are diagrams intended to recall the structure and operation of a conventional sampler-blocker, as well as the causes of distortions introduced by such a sampler-blocker
- Figure 5 is a diagram showing a blocker sampler provided with a distortion reduction device according to a first embodiment of the invention;
- Figure 6 is a diagram showing a blocker sampler provided with a distortion reduction device according to a second embodiment of the invention;
- Figure 7 is a diagram showing a first embodiment of an analog-digital converter including a blocker sampler provided with a distortion reduction device according to the invention
- Figure 8 is a diagram illustrating the shape of the modeled frequency response of the distortion reduction factor obtained for the analog-digital converter in the case of Figure 7
- Figure 9 is a diagram showing a second embodiment of an analog-digital converter including a sampler-blocker provided with a distortion reduction device according to the invention.

FIG. 1 schematically represents a blocker sampler using an electronic switch I controlled by a signal He of frequency equal to the sampling frequency Fe, and a capacitor Ce. The input voltage,
Ve, the sampler-blocker is applied to one of the terminals of switch I. The other terminal of this switch is connected to one of the terminals of the capacitor Ce, the other terminal of the capacitor Ce being put to the reference potential. The output voltage, Vs, of the sampler-blocker is that obtained at the terminals of the capacitor Ce.

 The operating principle of this blocker sampler is divided into two phases. The first phase consists in charging the capacitor Ce to the value of the input voltage by closing the switch. The second phase begins with the opening of the switch, at the end of the charging of the capacitor. The capacitor then maintains the voltage Vs, at the output of the sampler-blocker, constant.

 The switch I can be symbolized, as illustrated in FIG. 2, by a resistor Ri which has either a very low value, which corresponds to the closed state of the switch, or a very large value, which corresponds to the open state of the switch, the control signal He not having been shown here.

 The distortions made by a blocker sampler are usually harmonic.

 These harmonic distortions can be explained as follows, set out in relation to FIG. 3 which represents an assembly comprising, in addition to the elements represented in FIG. 2, namely the capacitor Ce and the resistance Ri symbolizing the switch, an amplifier- impedance adapter 100 said input amplifier disposed upstream of the resistance Ri and an impedance amplifier-adapter 200 said output amplifier arranged downstream of the common terminal to the resistance Ri and to the capacitor Ce.

At the sampling instants, that is to say at the closing instants of the switch, the amplifier 100 must supply a current, i, equal to
i = Ve - Vce (1)
Ri
where Vce represents the voltage of the previous sample.

 As the resistance Ri is low, for large variations in the input signal, the amplifier 100 can be made to operate in a non-linear regime, if the value of the current i given by the relation (1) is greater than the value maximum that can be delivered by this amplifier. This phenomenon is a cause of harmonic distortion on the output signal.

Also a cause of harmonic distortion, the non-linearity of the electronic switch can be interpreted and modeled as illustrated in Figure 4
- the resistance Ri during the closing time of
the switch depends on the input voltage Ve, i.e.
Ri = Ro + a Ve (where Ro denotes a fixed resistance and "a"
a coefficient expressed enrvvolt)
- the capacitor Ce has a resistance Re in
parallel on the capacity, called ideal, Ce.

The expression of the output voltage Vs at the end of the sampling time is then as follows
Vs = Ve. Re
Re + Ro + a Ve
As Ro (<Re, and with x = a, this expression can be written: Re
Vs = Ve 1
1 + x. Fr
or, after development limited to order 2
Vs = Ve - xVe2
which shows that the expression of Vs is not a linear function of the input voltage Ve.

 One solution to avoid reaching the maximum current of amplifier 100 would be to oversize it. Another more interesting alternative, and illustrated in particular in FIGS. 5 and 6 described below, consists in inserting between the input amplifier and the switch I, an integrating network R, C, which has the effect of attenuating current draws when the switch closes.

 A first solution to attenuate the distortions introduced by the electronic switch consists in feedbacking the output voltage Vs to the input voltage Ve, in the manner shown in FIG. 5 corresponding to the first embodiment of the invention, by means of a subtractor formed by a differential amplifier 101 associated with a set of resistors Ri, R2, R3, R4, the differential amplifier 101 also playing the role of the amplifier-impedance adapter 100 of FIG. 4 .

 More precisely, on the additive input, marked "+", of the differential amplifier 101 are applied on the one hand the input voltage Ve, through the resistor Rl and on the other hand the reference voltage, through resistance R2. On the subtractive input, marked "-", of the differential amplifier 101 are applied on the one hand the output voltage Vs, through the resistor R3, on the other hand the own output voltage V of the differential amplifier 101, through resistance R4. The output voltage Vs is taken at the output of a differential amplifier 201 mounted as an impedance adapter, disposed at the output of the sampler-jocker.

By asking
D = Re
Re + R + Ro + aV
let D = 1 l + x V
and with R3 = R4, R1 = R2
the expression of Vs as a function of V at the end of the sampling time is written
Vs = DV
We also have
V = - Vs + Ve
From where
Vs = Ve. D
1 + D
and, replacing D with its expression
Vs = Ve. 1 - xVs
2 - xVs
or, after dividing (l-xVs) by (2-xVs) by limiting the quotient to the order 1 Vs = Ve. (l - l xVs)
2 4
that is to say
Vs = Ve 1
2 1 + 1 xVe
4
or, after development limited to order 1 of 1
1 + 1 xVe
4
Vs = Ve - x (Ve
2 2 (2)
With an output voltage Vs equal, the feedback circuit according to FIG. 5 therefore introduces twice as little distortion as a circuit without feedback. However, this arrangement does not completely cancel the harmonic distortions, even by modifying the relationships between the resistors R1, R2, R3, R4.

 The arrangement shown in FIG. 6, corresponding to the second embodiment of the invention, theoretically makes it possible to completely cancel these harmonic distortions.

 In this arrangement, the output voltage Vs is feedbacked to the input voltage Ve, by means of a first subtractor, after having, in a second subtractor, subtracted from this output voltage Vs, the voltage output V of the first subtractor.

 This first subtractor is in this case produced by a differential amplifier 102 mounted as a subtractor by means of a set of resistors R'1, R'2, R'3 and R'4.

 This second subtractor is in this case produced by a differential amplifier 300 mounted as a subtractor by means of a set of resistors R5, R6, R7 and R8.

 More precisely, on the additive input, denoted "+", of the differential amplifier 300, the output voltage Vs is applied on the one hand, through the resistor R5, and on the other hand the reference voltage, to through the resistor R6, and on the subtractive input, denoted "-", of the differential amplifier 300, the output voltage V of the differential amplifier 102 is applied on the one hand, through the resistor R7 and on the other hand the own output voltage of the differential amplifier 300, through the resistor R8.

On the additive input, denoted "+", of the differential amplifier 102 are applied on the one hand the input voltage Ve, through the resistor R'1, and on the other hand the reference voltage, through resistance R'2. On the subtractive input, marked "-", of the differential amplifier 102 are applied on the one hand the output voltage of the differential amplifier 300, through the resistor
R'3, and on the other hand the own output voltage of the differential amplifier 102, through the resistor R'4. The output voltage V
s is taken at the output of a differential amplifier 202 mounted as an impedance adapter, disposed at the output of the sample and hold device.

With R'1 = R'2, R'3 = R'4, R5 = R6 and R7 = R8
the fitting equation is
V = Ve - (Vs - V)
Hence Vs = Ve
independent relation of D, which shows that this assembly makes it possible theoretically to cancel harmonic distortions.

 To avoid possible oscillation problems, a low-pass filter, not shown in the figure, can be placed between the output of amplifier 300 and resistor R'3.

It will also be noted that the assembly of FIG. 6 introduces a lower delay than that introduced by a conventional sampler-blocker. This can be explained as follows. A classic sampler-blocker has the transfer function
F (p) = 1 (1 -pTe)
p
where Te indicates the sampling period of this sampler-blocker, from which we deduce that the delay introduced by this sampler-blocker is equal to Te
2
The transfer function of the sample-and-hold feedback such as that of FIG. 6 would be written, in the general case of a feedback via a transfer function system M (p ) (which we considered for the representation in figure 6 as equal to the unit transfer function)
FR (P) = F (p)
1 - M (p) + F (p). M (p)
where M (p) denotes the transfer function of the sample and hold device without feedback.

 For M (p) tending towards 1, FR (p) tends towards 1, i.e. a delay tending towards 0.

 The present invention also aims to allow the production of an analog-digital converter including a sample-and-hold circuit, with low distortions.

 An analog-digital converter assembly with low distortions according to the invention is shown in FIG. 7 where an analog-digital conversion circuit has been identified, which is connected to the output of a sample-and-hold circuit, identified 36, which is in this case of the type represented in FIG. 6, with however a system, marked 40, of transfer function not necessarily equal to the unit transfer function, introduced between the output of the subtractor 300 and the input "-" of subtractor 102.

The transfer function of an analog-to-digital converter can be represented as follows
Are
X (z) a sampled analog input signal present at
converter input
Y (z) the digitally coded output signal on n bits
corresponding to the converter input signal
B (z) digital quantization noise
T (z) the transfer function of the noise-free converter
of quantification.

où xj représente un facteur de distorsion harmonique.We have then
Y (z) = X (z). T (z) + B (z). z
The transfer function T (z) of an ideal analog-digital converter without harmonic distortion is reduced to a delay function, i.e.
T (z) = -1
-1 -Tep
with: z 1 = e or Te denotes the period
signal sampling present at the input of
this converter
The transfer function T (z) of a real analog-digital converter, i.e. with harmonic distortion, can be modeled as follows

where xj represents a harmonic distortion factor.

We can then write

To simplify the expression, we can reduce this development to the first harmonic, i.e.
T (z) = z-1 (1 + x1 # X (z))
We obtain
Y (z) = X (z) # z-1 + x-1 # z-1 # (X (z)) + B (z) # z-1 (i)
In FIG. 7, the block 30 representing an analog-digital conversion circuit receives an input signal V (z) from, through the sampler-blocker 36 making it possible to stabilize this signal V (z) during its processing by this circuit. of analog-digital conversion, of a subtractor 31 which itself receives on its input "+" an incident signal A (z) and on its input "-" the signal from, through a system 33 of transfer function G (z), a subtractor 34 which itself receives on its input "-" the signal V (z) and on its input "+" the signal Y (z) of the output of circuit 30.

 To allow the feedback of the output of the analog-digital converter on its input used in this circuit, it is necessary to convert the digital signal from the converter into an analog signal. This operation is carried out using a digital-analog conversion circuit, not shown in FIG. 7. In what follows, it is considered that the distortions brought by this digital-analog conversion circuit are negligible compared to those brought by the analog-digital conversion circuit.

By approximating to 1 the transfer function of the sampler-blocker 36, the following expressions can be written for the assembly of FIG. 7
V (z) = A (z) - G (z) (Y (z) - V (z))
Y (z) = T (z). V (z) + B (z). -1
Using the superposition principle, the expression of Y (z) can be calculated as a function of A (z) then of B (z), the two relations obtained once added giving the expression of Y (z) as a function of A (z) and B (z).

The expression v (z) of Y (z) as a function of A (z) is given by the relation
V (z) = A (z) - G (z) (YA (z) - V (z))
with A = T (z). V (z)
and T (z) = -1 (1 + xl. V (z))
After the developments limited to the first terms, it comes

with H (z) = 1 - G (z) (1
The expression Y3 (z) of Y (z) as a function of B (z) is given by the relation
V (z) = - G (z) (B (z). Z 1 + V (z) T (z) - V (z))
-1
As Y (z) = B (z). z + V (z) T (z)
3
and as, given the order of magnitude of Y3 (z) by
-1
relation to YA (z), T (z) is equivalent to z, we obtain, in
replacing V (z) by its expression in the equation of
YB (z):
YB (z) = B (z). z 1 - G (z)
1 - G (z) (1 - z)
is
Y3 (z) = B (z). z. 1 - G (z)
H (z)
As Y (z) = YA (z) + YB (z)
we obtain for Y (z) the following expression

lG (z) + B (z) # z-1 #
H (z)
For G (z) close to 1, the expression of Y (z), compared to relation (i), shows that harmonic distortions and quantization noise are reduced significantly.

 However, the assembly presents a risk of instability, depending on the values of G (z).

 In the case where G (z) includes a real coefficient "g", that is to say in the case where G (z) is written in the form g. G '(z), a compromise must be found between the values of "g" and the cut-off frequency of the low-pass function G' (z) so as to obtain the best reduction factor while maintaining a sufficient margin of stability.

The reduction in distortions is linked to the frequency response of the function
R (z) = 1 - G (z)
1 - G (z) (1 - z)
is
R (z) = 1 - g. zx
1 - g. z (1 zl)
where zx represents the delay factor due to the low-pass function G '(z) and also to the sampler-blocker 36, and considering as negligible the attenuation due to the filtering of G' (z).

It is then noted that the closer x is to zero, the greater the reduction in distortions. Indeed, in frequency the modulus of R (z) is equal to

 FIG. 8 shows by way of example the shape of the function IR (f) I for g = 0.82 and x = 1.76 (curve C1) and for g = 0.82 and x = 0.76 ( curve C2), the curve C2 being in this case more favorable for the low frequencies, since the distortions are more reduced there.

 The assembly of FIG. 9 comprises, in addition to the elements already the subject of the assembly of FIG. 7, an additional feedback from the output of this analog-digital converter on its input, by means of a subtractor 50 which subtracts from the incident signal A (z), before application thereof to the “+” input of the subtractor 31, a signal originating, through a system 51 having a certain transfer function, from a subtractor 52, which itself subtracts from the output signal Y (z) the signal from the subtractor 50, which further improves the distortion reduction factor.

Claims (8)

1 / Device for reducing the distortions introduced by a blocker sampler, characterized in that it comprises means for feedback of the output of this blocker sampler, on the input of this blocker sampler. 2 / Device according to claim 1, characterized in that said feedback means comprise a subtractor (101) which subtracts at a voltage representative of the input voltage of this sample-and-hold circuit, a voltage representative of the output voltage of this blocker sampler. 3 / Device according to claim 1, characterized in that said feedback means comprise a subtractor (102) said first subtractor which subtracts, at a voltage representative of the input voltage of the sampler-blocker a voltage from d a second subtractor (300) which subtracts at a voltage representative of the output voltage of the sampler-blocker a voltage representative of the output voltage of the first subtractor. 4 / Device according to claim 2, characterized in that it further comprises an integrating network disposed between the output of said subtractor and the input of one sampler-blocker. 5 / Device according to claim 3, characterized in that it further comprises an integrating network disposed between the outlet of said first subtractor and the inlet of the sampler-blocker. 6 / Analog-to-digital converter, including a sampler-blocker provided with a device according to one of claims 1 to 5 and which delivers a sampled analog signal then converted to digital by an analog-to-digital conversion circuit that includes said converter, characterized in that it is further provided with feedback means from its output to its input. 7 / analog-digital converter according to claim 6, characterized in that the feedback means of the output of this converter on the input of this converter comprise a subtractor (31), said third subtractor, which cuts off the incident signal applied at the input of the converter, the signal coming, through a system (33) of transfer function G (z), from a subtractor (34), said fourth subtractor, which subtracts from the output signal of this converter the signal of output of the sampler-blocker, the latter receiving the signal from said third subtractor. 8 / analog-digital converter according to claim 7, characterized in that the feedback means of the output of this converter on the input of this converter further comprises a subtractor (50), said fifth subtractor, which subtracts from said incident signal the signal coming, through a system (51) having a certain transfer function, from a subtractor (52) said sixth subtractor, which subtracts from the output signal of the converter the signal coming from said fifth subtractor, this last signal being further applied to the input of said third subtractor.