Geiger-Müller Counter Circuit Theory

Geiger-Müller counter circuit theory 1: Basic structure of the Geiger-Müller (GM) counter blue LED HV supply GM tube inverter pulse stretcher piezo speaker filter red pump red LED difference amplifier green pump green LED A block diagram for the GM counter you will be building is given above. The purposes of these blocks are as follows: HV supply Converts the 9 V battery voltage to the 400 V needed by the GM tube. GM tube Detects ionizing radiation: emits a current pulse whenever an ionization event occurs inside the tube. inverter Converts the current from the GM tube into an inverted voltage pulse. pulse stretcher Converts the very short pulse from the inverter into a 1.5 ms pulse. blue LED Flashes every time a pulse occurs. piezo speaker Produces a click every time a pulse occurs. filter Accumulates charge from the pulses to produce a voltage roughly proportional to the count rate. red/green LED Displays a visual indication of the count rate that continuously fades from green to orange to red as the rate increases. red pump Drives the red LED with a current proportional to the voltage from the filter. difference amplifier Subtracts the filter voltage from a reference voltage to produce a signal that is goes down as the count rate goes up. green pump Drives the green LED with a current proportional to the voltage from the difference amplifier. The full schematic is given in Figure 1. By the end of this lecture you will understand the basics of how each of these blocks work. You will be equipped to understand the full details shown in the schematic by the end of 22.071. Geiger-Müller counter circuit theory 4 3 2 1 7_RT 4_FB 5_SCP 3_COMP 6_DTC 2_VCC 1_OUT 8_GND - 8 5 6 7 + 3 VI VO 1 1 2 3 4 5 6 2 3 1 4 3 2 1 7_DIS 4_RES 5_CTRL 3_OUT 6_THR 2_TRIG 1_GND 8_VCC 6 5 5 6 7 8 7 9 10 8 13 12 14 Figure 1: Full schematic for the GM counter. 2 VCC GND 4 11 2 1 2 3 2: Basic circuit concepts There are three quantities of interest in a circuit: charge A fundamental property of the particles that make up matter (protons, electrons, etc.). Charge is measured in units of coulombs (C). current The flow of charge through a wire or component. Current is measured in amperes (1 A > 1 C0s). Recall that an electron has a charge of −1.6 · 10−19 C: a current of 1 A corresponds to many electrons flowing per second! voltage The potential energy per unit charge. The units are volts (1 V > 1 +0C). Circuits are built up of components that manipulate the current and voltage in the desired manner. The most fundamental three components are: resistors Resist the flow of current: they dissipate the energy carried by the current. The voltage across a resistor is given by Ohm’s law: 7 > I3, where the resistance 3 is measured in units of ohms (volts per ampere, 1 Ω > 1 V0A). − + 7 3 I capacitors Store charge: the charge stored on a capacitor is 2 > C7, where C is the capacitance and is given in units of farads (1 F > 1 C0V). The time derivative of charge stored is the current through the capacitor: I > C d70dt. Note that the voltage across a capacitor must be continuous, otherwise an infinite current would be required! t>0 + − + 7s 3 7 C − I inductors Store magnetic flux: the flux in an inductor is ϒ > -I, where - is the inductance and is given in units of henries (1 H > 1 Wb0A > 1 V s0A). The voltage across the inductor is the time derivative of the flux: 7 > dϒ0dt > - dI0dt. Note that the current through an inductor must be continuous, otherwise an infinite voltage would be present! t>0 3 + − + 7s Geiger-Müller counter circuit theory 7 - − I 3 3: HV supply: the boost converter The boost converter takes the 9 V battery voltage and steps it up to 400 V. This is accomplished using an inductor and another very important component: the diode, a component which only permits current to flow in one direction. A basic boost converter looks like this: L + − + Vs C VHV load − The switch turns on and off rapidly, staying on for duration ton and off for duration toff each time. Consider the case when the switch is closed: L I L − + + VL Vs C VHV load − + − There can be no current through the diode in this case, so the capacitor is what provides current to the load. The voltage across the inductor is equal to the supply voltage: VL = Vs . So, the current in the inductor is increasing according to V t V dIL = s → ΔIL,on = on s dt L L Now, open the switch: L I L + − + Vs VL − + C VHV load − Recall that there can be no discontinuity in the inductor current – the current now flows through the diode to both charge the capacitor and power the load. But, the voltage is free to change instantly: it is now given by VL = Vs − VHV . During this period the current in the inductor therefore drops according to V − VHV t (V − VHV ) dIL = s → ΔIL,off = off s dt L L For the circuit to operate in steady-state, the current must come back to the same value after each cycle: ΔIL,on = −ΔIL,off → ton Vs t (V − VHV ) t +t V 1 = − off s , → on off = HV = Vs 1−D L L toff where D = ton /(ton + toff ) is the duty cycle. Since 0 ≤ D ≤ 1, the output voltage is always greater than or equal to the input voltage. The actual circuit uses a chip called the TL5001 to actively control D in order to maintain the desired output voltage. Geiger-Müller counter circuit theory 4 4: Side note: measuring the high voltage For energy to be conserved, the current to the load has to be smaller than the current drawn from the battery. But, measuring devices such as multimeters and oscilloscopes have large (but finite) input impedances and can draw too much current, thus causing the output voltage to drop. Therefore, to get an accurate measurement of the voltage applied to the GM tube it is necessary to use a voltage divider: R1 I Vout VHV VHV VHV = I(R1 + R2 ) → I = R1 + R2 R2 R2 Vout = IR2 = V I R1 + R2 HV As long as the total resistance, R1 + R2 , is sufficient to not load down the boost converter, an arbitrary division can be obtained. But, the meter itself has a resistance RM , so the circuit actually looks like this: R1 I Vout VHV R2 RM The analysis proceeds as before, but R2 and RM must first be replaced with their equivalent resistance, Req = R2 RM /(R2 + RM ). Multimeters typically have an input resistance of 10 MΩ, while oscilloscopes typically are only 1 MΩ. Therefore, the GM counter includes a jumper to select which measuring device you are using. 5: Inverter The GM tube emits a current pulse, but the subsequent circuits require a voltage pulse. This conversion is accomplished simply by putting the current from the GM tube through a 5.1 kΩ resistor. But, as will be discussed in the next section, the pulse stretcher actually needs the inverse of this pulse – a signal that sits at Vs = 5 V when nothing is happening, then temporarily drops to 0 V when a pulse happens. This conversion is accomplished using a transistor. In more advanced settings you can use a transistor as an amplifier, but we will simply be using it as a switch. The transistor has three leads: the emitter (e), collector (c) and base (b): c b e When Vb > Ve , current can flow from c to e. But, when Vb < Ve no current can flow. Geiger-Müller counter circuit theory 5 Therefore, an inverter can be constructed like this: Vs Vout Vin When Vin is high, current can flow through the transistor and Vout is pulled low. When Vin is low, current cannot flow and Vout is pulled to Vs . 6: Pulse stretcher The output from the GM tube (and hence the inverter) is very brief – if it were used to drive the piezo speaker and blue LED directly, the effect would be nearly imperceptible. The pulse stretcher uses a very useful component known as a 555 timer to turn a short input pulse (of arbitrary shape and duration) into a square pulse 1.5 ms long. The 555 timer is a circuit building block that brings together several related functions in one convenient device. For those familiar with comparators and flip-flops, a simplified internal schematic is given in Figure 2a. Refer to Figure 2b and Table 1 for the locations and functions of each pin. Refer to Franco [1], Horowitz and Hill [2], and manufacturer data sheets such as [3] for more details on this. The pulse stretcher is formally known as a monostable multivibrator, the implementation is shown in Figure 3. Because of the structure of the timer, the pulse input to TRIG must be falling – i.e., the signal starts out above 1/3 VCC , then drops below that level to trigger a pulse. This is why the inverter is necessary. To understand how the circuit works, first consider the state before the pulse arrives: • There is no current from the tube, so the inverter puts Vs at TRIG. • The timer has not yet been triggered, so OUT is at 0 V. • DISCH is conducting, and hence the capacitor C is drained of all charge. Once the pulse arrives: • The voltage at TRIG briefly drops below 1/3 VCC . • This causes OUT to be set to VCC . • This also causes DISCH to stop conducting. • Hence, the capacitor C starts to charge through resistor R. • After ton = 1.1RC, capacitor C is charged to the point that THRESH is above 2/3 VCC . • This causes OUT to be set to 0 V and DISCH to become conducting, thus rapidly draining the capacitor and getting the circuit ready for the next pulse. Sample voltage histories for a single triggering of this circuit are given in Figure 4. Geiger-Müller counter circuit theory 6 8 Vcc Figure 2: (a) Simplified internal schematic of the 555 timer. Figure inspired by [1]. 4 RES R (b) Pinout of the 555 timer in an 8-pin DIP package. + THRESH 6 C1 - CONTROL 5 CL R R Q 3 OUT flip-flop S Q + C2 - TRIG 2 GND 1 8 Vcc TRIG 2 7 DISCH 555 R GND 1 OUT 3 6 THRESH RES 4 5 CONTROL DISCH 7 (a) internal schematic (b) pinout Table 1: 555 Pin Descriptions Pin Name Function 1 GND Ground connection. 2 TRIG Trigger: when the voltage at this pin drops below 1/3 VCC , the flip-flop is set, which sends OUT high. 3 OUT Output: turns high when TRIG drops below 1/3 VCC , turns low when THRESH rises above 2/3 VCC . 4 RES Reset: when the voltage at this pin goes low, the flip-flop is reset, therefore setting OUT to low regardless of the conditions at TRIG or THRESH. 5 CONTROL Control voltage: accesses the internal voltage divider, allowing you to modify the thresholds to some extent. 6 THRESH Threshold: when the voltage at this pin rises above 2/3 VCC , the flip-flop is reset, which sends OUT low. 7 DISCH Discharge: when the flip-flop is on (OUT is high), there is no base current and the transistor does not conduct. When the flip-flop is off (OUT is low), the transistor is turned on (saturated), thus allowing an external capacitor to be discharged to ground. 8 VCC Power supply. Geiger-Müller counter circuit theory 7 VCC Figure 3: Monostable multivibrator (one-shot pulse stretcher) implemented with a 555 timer. R VCC 10nF C vTRIG [V] The top plot shows the voltage at pin 2 (TRIG). Notice that the pulse does not need to drop all the way to zero, nor does it even need to have a particularly “square” shape – as soon as vTRIG drops below 1/3 VCC the cycle starts. 4 2 vOUT [V] 0 4 2 The middle plot shows the voltage at pin 3 (OUT). The pulse starts as soon as the voltage at pin 2 (TRIG) drops below 1/3 VCC and continues for a duration 1.1RC. 0 4 vC [V] Pin 5 (CONTROL) is connected to ground through a 10 nF capacitor in order to reduce the impact of noise in the circuit on the threshold voltage. Figure 4: Voltage histories for the monostable circuit. Monostable Multivibrator, RC = 1ms, Vcc = 5V 2 0 −0.5 Pin 4 (RES) is held to VCC in order to keep the flip-flop enabled. 0 0.5 1 t [ms] Geiger-Müller counter circuit theory 1.5 2 The bottom plot shows the voltage across the capacitor (and hence at pin 6 (THRESH)). The pulse ends and the capacitor is rapidly discharged through pin 7 (DISCH) as soon as vC reaches 2/3 VCC . 8 7: Op-amps The op-amp (short for “operational amplifier”) is an exceedingly versatile component – it can be used to construct many types of filters and amplifiers, among other things. The op-amp has three terminals of interest: V− − V+ + Vout There are two simple rules that enable you to work out what many op-amp circuits do: 1. There is no current in or out of the “+” and “−” inputs. 2. When negative feedback is present, the op-amp will adjust the voltage at the output terminal to ensure that V+ = V− . Consider the non-inverting amplifier: R1 − Vout R2 + Vin From rule (2), we know that V− = V+ = Vin . From rule (1), we know that all of the current goes from the output to ground, since it cannot go into the “−” input. Notice that R1 and R2 form a voltage divider, so Vin = R R2 Vout → Vout = 1 + 1 Vin ( R1 + R2 R2 ) 8: The filter The filter acts to smooth out the pulses from the GM tube in order to produce a voltage roughly proportional to the count rate. It is of a very simple type: R1 − Vin R2 Vout + Rfilter Cfilter This is simply the non-inverting amplifier from above with a filter composed of Rfilter and Cfilter added to shunt the high-frequency components off to ground. Geiger-Müller counter circuit theory 9 9: The current pump The brightness of the LEDs is determined by the current. But, the filter described above puts out a voltage. A circuit that converts a voltage to a current is called a transconductance amplifier. The GM counter uses a particular implementation known as the Howland current pump: R4 R3 − + R2 Vin R1 load Iout As long as R R4 = 2, R1 R3 the current delivered to the load will be Iout = Vin R1 10: The difference amplifier The filter and one current pump are sufficient to drive a current through the red LED which is (roughly) proportional to the count rate. But, to have the desired effect the green LED must fade out as the count rate increases. A difference amplifier is used to subtract the filter voltage from a reference voltage: R2 V1 R1 − Vout + V2 R3 R4 Geiger-Müller counter circuit theory 10 If R3 = R1 and R4 = R2 , then the output voltage will be Vout = R2 (V − V1 ) R1 2 References [1] S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed. McGraw-Hill, 2002, ch. 10.3. [2] P. Horowitz and W. Hill, The Art of Electronics, 2nd ed. Press, 1989, ch. 5.14. Cambridge University [3] Texas Instruments, “LM555 Timer Datasheet,” SNAS548B. Geiger-Müller counter circuit theory 11