Designing the controller for a thermoelectronic source. Giorgio Fontana University of Trento

Transcription

1 Designing the controller for a thermoelectronic source Giorgio Fontana University of Trento

2 The aim of this presentation is to illustrate the design workflow for a filament controller intended for a thermoelectronic source. An identical workflow is applicable to a thermoionic source, the only difference being the sign of the controlled current. A typical design for a thermoionic source is the following: Set Point for the Ion Current Approx. current A Closed Loop Controller for Electron-Beam Evaporators Alan Band and Joseph A. Stroscio Electron Physics Group National Institute of Standards and Technology Gaithersburg, Maryland 20899

3 Our Design Goals 1. Simplest Circuit 2. Fully analog circuit with ability of computer control or manual control 3. Modular approach with redesignable building blocks 4. Capability of applying offset voltages to beam intercepting grid 5. Capability of applying offset voltages to the emitting filament 6. Main signal processing referred to system /laboratory ground 7. Possibility to exchange analog processing with digital processing while keeping the remaining modules compatible.

4 Principles of Feedback Control Direct Control: Manual control Filament Thermo- Electronic current Instrument + Error Measured Thermo- Electronic current Gain K in + out out=k(in-out) out(1+k)=k in out=in K/(1+K) Gain K err out Control signal and Error signal in a Feedback system out=err-kout out(1+k)=err out=err /(1+K) Manual control + - Gain K Filament Thermo- Electronic current Instrument + Error Measured Thermo- Electronic current Feedback Control: If K>>1 then Output Input (Manual Control) Error Direct Control Error/K Note: With feedback control, gain (filament working point) changes make negligible effects.

5 Dominant Pole The feedback control has by definition a signal loop. Oscillations may occur if along the signal loop the phase shift is 180 and gain =1 (0 db). Each low pass element: RC circuit, thermal time constant, etc, introduces one or more poles in the loop transfer function. If in the region where the loop gain is >=1 contains only one real and negative pole, the closed loop system is unconditionally stable. Obviously the gain and the ability of the control system to suppress errors are now a function of frequency. Bode diagram of a low pass RC network followed by a 60 db (1000x) gain. The phase delay is between 0 and -90. In a closed loop this low pass network is always stable for any gain. A low frequency dominant pole is often used to make the transition to 0 db within the 0-90 phase range.

6 The Electrometer or I V Converter or Transimpedance Amplifier (TIA) floating The I/V converter converts the electric current coming from the grid to an output voltage. It also keeps the voltage of the grid respect to the ground (ground symbol laboratory ground) equal to the Grid Bias Voltage that is externally imposed. The output voltage Output is defined respect to the Reference Voltage for the Output. This is a well known circuit, where pin 2 of the OPAMP is a virtual ground respect to pin 3 of the OPAMP. The output voltage is defined by Vout=- Igrid*R1 with good accuracy. Detailed analysis of the I/V converter (TIA) can be found here: where the capacitance of the Grid and the details of the OPAMP are taken into account. If R1 is larger than ~1 Mohm a FET input OPAMP should be employed. R1 must have a value in order to provide 10 V Output with the maximum design Grid current. The power supply must be floating.

7 The Level Shifter The level shifter is a differential amplifier. The voltage difference between the two inputs is transferred to the output, whose voltage reference is the ground symbol. This circuit is powerd by a power supply (+15 V and -15 V) referenced to the ground symbol that is laboratory electrical ground. Because of the negative feedback the two inputs of the OPAMP are at the same potential determined by Vin+. OPAMP inputs must not be outside the interval +10 V -10 V, therefore because Vin+=Vref*R4/(R6+R4)=Vref*1/21, we have that Vref (Grid Bias Voltage) must not be outside the interval -210 V to +210 V. This Level Shifter attenuates the differential input by 20: Vout=(Reference for Input Voltage Input Voltage) * R3/R5, with R3=R4 and R5=R6. See Millman and Halkias Microelectronics. The Input and reference Voltages can be interchanged to invert phase. Note: all 50 Ohm resistor are not necessary if no coaxial cable is used. If used, subtract 50 from the following resistor.

8 The Pole Zero Controller With the grid capturing an e- current, the output of the electrometer is positive respect to its reference and the output of the level shifter becomes negative respect to ground. The PZ controller inverts the phase again, and its output is in phase with the e- current. We will consider this fact for obtaining an overall negative feedback. Vin- of the OPAMP is a virtual ground. With +10 V maximum from the I/V Converter and a factor of -20 from the Level Shifter, the minimum Input Voltage of the PZ Controller is V. This is a gain limited integrator with a zero in its transfer function (τ=r10*c1), the zero should cancel the pole due to the filament thermal time constant, thus reducing the sistem to first order with a simple exponential response in a feedback loop.

9 The Pole Zero Controller 2 Vin- of the OPAMP is a virtual ground, it will stabilze to laboratory ground potential, therefore because Input Voltage is between 0 and -0.5 V, we choose a Control Voltage proportional to the Input Voltage with a minus sign and in the interval 0 V to 10 V. We therefore have 0.5/10 = R8/R9, with currents IR8=-IR9. The Control Voltage sets the grid current. The DC gain of the controller is R11/R8. The high frequency gain is R10/R8. The dominant pole time constant is R11*C1. The time constant of the zero, that must cancel the pole introduced by the thermal time constant of the filament is R10*C1. For any frequency the gain of the above controller must be lower than the open loop gain of the operational amplifier by not less than 20 db, in order to have that the transfer function of the PZ Controller is determined only by the capacitors and the resistors of the above circuit, this criterion can be used for determining R11. Note: OPAMP parameters may change from sample to sample.

10 The Pole Zero Controller 3 With the component values of the previous slide, we have the above modulus of the transfer function. The green curve is the frequency response of the Pole Zero Controller. The red curve is the open loop frequency response of the OPAMP. The y scale is in db. The dominant pole is at about.001 Hz. The zero is at about 1 Hz. The high frequency gain is 1 (0 db).

11 Optoisolated Filament Driver floating With a LED-Phototransistor isolated coupler characterized by BJTcurrent/LEDcurrent=10, considering the above design we have that 1V from the PZ Controller will produce 10V at the output of the OPAMP. R13 will also limit LED current to 1 ma. R12 and R13 depend on the detailed specifications of the Photocoupler and the required gain. The Power Darlington TIP 102 is connected as emitter follower and can provide a couple of A current to the filament in the voltage range 0-10V. A limiting resistor could be connected in series to the filament if necessary. Increasing LED current will produce increasing filament current. A convenient location for the loop phase inversion is between the PZ Controller and the LED. No cross is needed for obtaining a negative feedback for this example.

12 The DC Loop Gain Suppose that near the operating point of 5 ma of electron current, the filament is characterized by 1 ma/v of transfer characteristic, and that we want 10 ma maximum electron current. (Please Note that common OPAMPs cannot manage more than about 20 ma in this simple electrometer configuration) The electrometer feedback resistor must be 10 V (fixed limiting value for us) / 10 ma (maximum electron current) -> R1=1 kohm. The OPAMP can be of the BJT input type. The combined voltage to voltage transfer characterstic of the filament and the electrometer is A/V * 1000 V/A = 1. The voltage gain of the level shifter is 1/20 = 0.05 The DC voltage gain of the PZ Controller is 60 db = R11/R8 = 1000 The voltage gain of the Filament Driver is 10 The loop gain is 1*0.05*1000*10 = 500. Therefore fluctuations of the emission are reduced by a factor of 500 respect to an open loop control. Changes of the loop gain K due to different working points of the filament are strongly suppressed because they enter the transfer function through K/(1+K). Note: It is possible to increase the loop gain by increasing R12, and or by increasing R11.

13 Thermoelectronic Emission In 1901 Richardson published the results of his experiments: the current from a heated wire seemed to depend exponentially on the temperature of the wire with a mathematical form similar to the Arrhenius equation. Later, he proposed that the emission law should have the mathematical form,where J is the emission current density, T is the temperature of the metal, W is the work function of the metal, k is the Boltzmann constant (Source Wikipedia) The temperature of an in-vacuum tungsten filament as a function of current. From the data of Jones & Langmuir with an approximating curve. The x-axis is the current divided by the diameter of the wire (in cm) raised to the 3/2 power. A Richardson Plot of thermionic emission in a FP-400 vacuum tube. Each data point displays the plateau anode current at a particular filament temperature. The curve through the data fits for the work function; the slightly steeper curve uses the book value for the work function.