This chapter describes the design of the current amplifier, the problems during the realisation and same solutions for the problems.
4.1 Specifications
We want to design a current amplifier that can supply both the actuating current and the sensing current to the coil. The actuating current must be large enough to keep the ball levitated and must be handlimited to avoid very high volta.ges to he induced in the cail. For accurate sensing it is necessary to keep the current of the sensor constant. So the current amplifier has to satisfy the following equation and frequency spectrum (see figure 4.1).
icur.amp = iaet1lator
+
isensorsinwt This results in the following specifications:IHIt - - - .... j .
(4.1)
:' fa.lUalor fsensor freq
Figure 4.1: Desired spectrum of the current amplifier
• The maximum current, which must be provided by the amplifier, is estimated with some simulations (see section 5.4). For a small motion around an equilibrium point Xo
±5[mm] of the ball a current of 2[A] appeared to be sufficient with some peak currents of Iess then 3 [A]. This means a current amplifier must be designed that can supply a CUfrent of at least 3 [A] .
• The simulations mentioned above showed a voltage supply of about 30 [V] was sufficient to realize the currents needed to levitate the ball.
22
CHAPTER 4. A CURRENT AMPLIFIER 23
• It is very important to keep the sensing current constant, as explained in chapter 3. If the sensing current is supplied behind the amplifier (figure 4.2) the output-impedance of the current amplifier must be high. Ifwe want to use the other method, applying the sensor current at the input of the amplifier, it is necessary that the bandwidth of the current amplifier must be at least fsen Hz. However, this means very high voltages will occur, which may cause instabilities .
• The bandwidth that is needed to keep the balllevitated is about lOOHz,as the dynamics of the levitation system are also bandlimited at this frequency. To avoid instabilities of the amplifier it is necessary to use the fact that no high frequent currents are needed.
This results, together with the earlier item, in the desired spectrum of figure 4.l.
In the next section wewill start from a basic circuit that is used asa current amplifier. After that we will show the problems that occurred using this circuit, when the current was supplied to a coil (large inductive laad)
4.2 The basic principle
The circuit that we started from is shown in figure 4.2. This circuit consist of a fet (MOS field-effect transistor) driven by an opamp (operational amplifier) and a source resistor Rs which voltage is fed back to the input of the oparnp.
Vin
(4.2)
.Vee .15V
Figure 4.2: The basic scheme of the current amplifier
The opamp causes the souree voltage to be equal to the input voltage. The drain current will be
I Vee - Vin
d=
R
sThis equations only holds wh en the gain of the opamp is very high (Ao ---+ 00) and the fet is in the saturation region (Ves - VThreshold ~ VDS).
The output impedance of this current amplifier is Aa
Zoutput '" 1 .R s .afet
+
T· S (4.3)where
a/et = constant of the fet (in saturation: ID :::::J a .VDS)[']
1" = time constant of the opamp[s]
Ra
=
source resistor~ 0.2[n]In (4.3) we can see that Zo decreases if s increases. Furthermore the impedance of the coi1 increases if sinereases. This means that the amount of sensing current that will really enter the coil will depends on the frequency and on VDS,as a depends on VDS. The earlier rernarks imply that the sensing current will not be constant in thisci~cuit.
Some further remarks can he made about this circuit:
• After the realisation of the amplifier it turned out that instabilities occurred when supplying a current to the coil. This can be corrected by decreasing the handwidth of the opamp. But when the bandwidth of the opamp is decreased a1so the gain for high frequencies is decreased and this will affect the output impedance negatively.
• Ifa conventional opamp is used, for examp1e J.LA741 or LM308, it is necessary to connect the hot tom of the coil to the negative voltage supp\y to get a sufficient range for the coil voltage. This makes the sensor system more complicated. Another disadvantage of using a conventional opamp is that the ideal region of operation for the output voltage is around OV and here the opamp is operating just below the positive voltage supply.
Because a conventional opamp is 1ess suitab1e for this application, we looked for a more ded-icated opamp and found one, the XTRllO.
The XTRllO is a highprecision voltage-to-current converter which can easily be used as a current amplifier by adding an external mosfet and source resistor. This will be called thë U-I converter from now on. The XTRllO has the following specifications [1]:
• Single supply operation and wide supply range: 13.5V to 40V
• Selectabie output range, dependent on the external components
• Very high output impedance (109), if fet is in saturation region.
Moreover , a suitable mosfet has been selected after we checked for the following criteria:
• The maximum drain-current.
• The minimum VDS needed to keep the fet in it's saturation region.
• The maximum permissible power dissipation
We have chosen the IRF? 9140 [2]. The maximum drain current is 19A and the maximum power dissipa.tion is 15üW. The fet has to he cooled with an appropriate heatsink in comhi-nation with foreecl air rooiing (e.g. a ventilator). Otherwise the fet will he damaged due to the enormous power dissipation.
In the next seetion we will analyze the U-I converter.
CHAPTER 4. A CURRENT AMPLIFIER 25
4.3 The U-I converter:
In figure 4.3 the complete circuit of the U-I converter is shown.
Cd
r---Figure 4.3: The scheme of the U-I converter
The operation of this circuit is almost the same as the basic circuit. Only a subtraction circuit is placed at tbe input. The sta.tie transfer function is
fd R2R3
Uin = (Rl
+
R2)R4R~ (4.4)The c1amping diode, parallel with the coil, is of great importance. The diode avoids negative voltages over the coil. Ifthe diode is not present negative voltage-peaks will cause all kinds of undefined non-linear effects of the fet and a limit-cycle occurs.
Even with the c1amping diode we see an oscillation at the coil voltage (see figure 4.3).
The frequency and the pulse-width of this oscillation depend on the voltage supplyand the
, lito
Figure 4.4: The oscillation of the coil voltage
coil current. With a supply of 40 V and a drain current of IA the frequency is about 250 Hz.
Another observation wemade, was that the oscillation is largely damped when the sensor system is connected to the cail. The first part of the sensor system is a first order high pass filter (see Cd and Rd in figure 4.3). The frequency and amplitude of this sinusoidal oscillation
also depends of the voltage supplied and the coil current. The frequency is about 16 kHz and the amplitude is 10V.
In the next sections we will explain these observations by means of some simulations and measurements. Finally we will give a solution for these problems.
4.4 Analysis and simulation of the U-I converter
4.4.1 Simulations with Spice
For the simulation of the U-I converter we used the software package Spice. Spice is a simulating program for electronic circuits. The circuit is described by it's junctions and components. A lot of analysis can be done with Spice. Same analysis we used were:
• DC-analysis, determine the input/output characteristic.
• Transient analysis, analysis in time.
• AC-analysis, ca1culate the complex transfer function based on linearized small signal models at the operating point.
The opamps of the U-I converter are modelled with a first-order model:
Vout = 1
+~o/wo
(V+ - V_) (4.5)where Ao is the open loop gain and Wo is the open loop bandwidth (wo
= *).
Becausethere were na specifications of the opam ps in the datasheets of the U-I converter, we measured the closed loop transfer function of the oparnps:
Hel = 1 (4.6)
1
+
s/AowoThe closed loop bandwidth is Aowo ~ 3 .106rad/ s. Sa we consider that Ao :::: 1 . 105 and
Wo :::: 30rad/ s. These values match with the specifications of conventional oparnps.
The transistor of the U-I converter has been modelled as a standard NPN-transistor of Spice. The power mosfet is modelled as a standard p-enhancement MOS fet with some ad-ditional parameters, such as input- and output capacitance, drain resistance and inductance and transconductance parameter.
First we simulated the U-I converter with a resistor as load, in figure 4.5 the AC-analysis is shown.
In this figure we see that one pole, s}
=
-3.106 [rad/sJ, is equal to the pole of the opamp's and the other one, 82 = -1.2· 106 [rad/s], is a little bit smaller, caused by the fet. So the bandwidth of the system is about 200 kHz.The next simulation is the analysis of the U-I converter with an inductive laad, see figure 4.4.1. In figure 4.6(a) the transfer function
ijL
is shown and in figure 4.6(b) the transferreJ
function ....1L.Ur.J
In these figures we see that the coil voltage increases extremely the frequency is enlarged and that the bandwidth ofthe system is decreased to 10 kHz. The frequency (16 kHz) of the sinusoidal oscillation mentioned in section 4.3 is approximately the same as the frequency (10 kHz) of the resonance peak.
CHAPTER 4. A CURRENT AMPLIFIER 27
0.11111",_nn:101271eS 18:21:32
A 10 --- -- -.- --. -- - -- -- --- -.- -- --- ---.-.-- ••• - - --.--- •••
---·10
..-0 +- _._ ..~- - w _••-r -_ --"" _. -r" _ - -r-.-" ---- -1
1.01'1 tOh tOCh 1.Okh 10Kh fOOKh 1.0Mh
• 20'log(v(7J)
Figure 4.5: The AC-analysis of the U-I converter with load resistor, Ure! - t ULo
T~""270 A 200T-"""" ---....~..._._ e . . . .- . . . " • • " " . '--~._. . . - - - .. - . . . • . . . .w - . - _ . . .0_' 0_;
1~ ~
oT·..•·..·· --- _.e_0 _ 0. . - - -.. - - -- ·"1
100~
,.,., ,.",
lOOI>
, ,
-250+ _-.. --.-- ••••• _ •••••• __ - ••• - ••····.--_···4
0·--..···.. ·--··-_··· --- --.,.- --- - ".- ,
,Oh 10t1 10Cfa
·20~)
Figure 4.6: The AC-anaJysis of the U-I converter with inductive load 4.4.2 The analysis
The oscillations of the U-I converter are caused by very small disturbances in the current.
These dist urbance will be amplified strongly by the cail. The puJses in figure 4.:J are probably
caused by disturbances of the power supply or noise in the souree resistor. Because of these disturbances, the cail voltage is increased to the voltage supplied very fast and the drain current becomes zero as the fet is closed (VDS
=
0). When the RC-network of the sensor system is connected the high frequency disturbances will be damped. The impedance of the RC-network is smaller than the impedance of the eoil for high frequencies.Another explanation for some problems is that a system containing a current souree in series with a coil is not a causal system. The coil wants to control it's own current (h =: JUL dt) and that is contradictory to the current souree. By adding a RC-network a causal system is obtained, now the eurrent souree and thecoil can bath control their currents.
4.5 The solution
We must ehoose Rd and Cd of the RC-network sa that the unwanted high frequency dis-turbances are damped and that the cantrol current (J
<
100Hz) and the sensor signa!(lkHz
<
fs<
2kHz) are not influeneed by the network. This means,ZL+RL
»
ZCd+RdZL+RL
«
ZCd+Rdif
f <
5kHzandif
f>
5kHz.This results in Rd =: 1k!1and Cd = 18nF. The load of the amplifier can now be written as (4.7) The zeros of this function are: Zl =: -44 rad/ s
Z2 == -56· 103 radjs
The poles are: P},2 =: -5· 103
±
j23 .103 rad/ sThe poles and zeros of this system correspond to the poles and zeros shown in the AC-analysis of spice (see figure 4.7).
We also measured the transfer functions of the whole system with a spectrum analyzer.
The result of this measurement was the same as the result of the Spice simulation.
Because the bandwidth of the amplifier has to be large due to the sensor current there is still some noise of the smal1 souree resistor that will be amplified. This noise disturbs the sensor signa!. It is better to add the sensor current behind the amplifier. The advantage is now that when the fet is closed (Id =: OA) the sensor signal is not disturbed by the amplifier.
4.6 Conclusions
In this chapter we tried to design a curTent amplifier that was able to supply bath the actu-ating current and the sensing current to the cail. This resulted in the ideal spectrum shown in figure 4.1. However, in practice, it is not possible to realize sneh a transfer function.
This meant the bandwidth of the amplifier had to be at least fsen to be able to supply the sinusoidal sensing eurrent to the coil with a constant amplitude. However, this bandwidth appeared to be too large to avoid instabilities. These were eaused by the large inductive laad
CHAPTER 4. A CURRENT AMPLIFIER 29
1~270
~1
~1
,~
1
"'1 '
.~ 1 :
.240+._ •• --.o· .. ·r -._ --r" . - .0 · .. · _ _ _ _ .. ,_ _ . 0 • • • •t
lOh 11»'1 lOOPt 101<h 1010'1 10010'1 1~
.20"a:)g(l(l1))
A -0I-·.·--··.·--·--····--·----···--·.··---·.·.·---·.·--_···~_··_---·_·-1 llft'O«lkn. 71 0
.
.
o .-- ••••••••••••••••• -_ ,. __ •••••••••. --_ ••.••••••• __ ••••••••
't)h 1~ 1oc;», ,(I(h 1lJOl lootO'l 1tNl\
. ~
A 110T··· ..···..··· -:
~ j
j 1
120
i .. \
Figure 4.7: The transfer function of the U-I converter
(the cail) that extremely amplifies high frequent currents. Therefor it was better to supply the sensing current behind the amplifier as shown in figure 4.3. However, this means the output impedance of the current amplifier must be large enough. The bandwidth of the actuating cur-rent through the coil has been restricted by the RC-network parallel with the coil in figure 4.3.
Up till now we have designed a "system" that supplies the sensing current and actuating current separately. However, even in this system it is very hard to sense as the sensing current is disturbed by noise generated in the current amplifier.
(5.2) (5.1)