Amplifiers in systems

Amplifiers in systems Amplification single gain stage rarely sufficient add gain to avoid external noise eg to transfer signals from detector practical designs depend on detailed requirements constraints on power, space, cost in large systems e.g. ICs use limited supply voltage which may constrain dynamic range Noise will be an important issue in many situations most noise originates at input as first stage of amplifier dominates often refer to Preamplifier = input amplifier may be closest to sensor, subsequently transfer signal further away In principle, several possible choices V sensitive I sensitive Q sensitive g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 1

Voltage sensitive amplifier As we have seen many sensors produce current signals but some examples produce voltages thermistor, thermocouple, opamp voltage amplifier ideal for these especially slowly varying signals few khz or less For sensors with current signals voltage amplifier usually used for secondary stages of amplification Signal V out = Q sig /C tot C tot = total input capacitance Noise C tot will also include contributions from wiring and amplifier V out depends on C tot not desirable if C det is likely to vary eg with time, between similar sensors, or depending on conditions to be discussed more later contribution from amplifier, and possibly sensor S/N = Q sig /(C tot.v noise ) can it be optimised? C det en vo g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 2

Current sensitive amplifier Common configuration, eg for photodiode signals f = Av in v in = i in f = [A/(A1)].i in f i in f Input impedance v in = i in f /(A1) Z in = f /(A1) i in v in gain A Effect of C & in consider in frequency domain v 0 = i(1/jωc in ) = i(ω)/(1 jωτ) i C i in input signal convoluted with falling exponential increasing f to gain sensitivity will increase τ fast pulses will follow input with some broadening Noise will later find that feedback resistor is a noise source contributes current fluctuations at input ~ 1/ f g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 3

Charge sensitive amplifier Ideally, simple integrator with C f but need means to discharge capacitor large f i in Cf Assume amplifier has Z in very high (usual case) = Av in v in = i in /jωc f = [A/(A1)].i in /jωc f i in /jωc f => Q/C f Input impedance i sig t Q/C f t v in = i in /(A1)jωC f C=(A1)C f at low f so amplifier looks like large capacitor to signal source low impedance but some charge lost e.g. A = 10 3 C f = 1pF isig C tot (A1)C f Q A = Q/[1 C tot /(A1)C f ] C tot = 10pF Q A / Q =0.99 C tot = 100pF Q A / Q = 0.90 g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 4

Feedback resistance f Must have means to discharge capacitor so add f Z f = f 1/jωC f iin C f = [A/(A1)].i in Z f = i(ω) f /(1 jωτ f ) τ f = f C f step replaced by decay with ~ exp(t/ f C f ) τ is long because f is large (noise) easiest way to limit pulse pileup differentiate ie add high pass filter Polezero cancellation exponential decay differentiation => unwanted baseline undershoot introduce canceling network v 0 = 1/(1 jωτ f ) v 1 = 1/(1 jωτ f )(1 jωτ 1 ) f C f p t τ 1 = C < τ f add resistor p so p C = τ f then C v 1 ' = 1/(1 jωτ 3 ) with τ 3 = ( p )C < τ f g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 5

Effect of finite bandwidth ealistic input stage of amplifier = i d ( L C L ) i d = g m v in loga A0=gmL A = g m L low f A = g m /jωc L high f input (NB phase change) L C L logω ω 0 = 1/ L C L ω h =g m /C L Z in 1/A.jωC f = C L /g m C f resistive! Irrespective of detailed design i sig A A 0 ω h /jω = 1/A 0 ω h C f ω h = gainbandwidth product C det in i in Effect of in signal current shared between in & C det = i in Z f i/[jωc f (1 jωτ rise )] v o ~ 1 exp(t/τ) τ = in C det t high frequencies in leading edge leading edge of output pulse g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 6

Output impedance Usual method of varying and finding i out generally messy algebra Current sensitive amplifier, open loop gain = A = i 2 ( 2 in ) v in f i f i 2 = i f 2 = f v in = i 2 in v o = Av in = Ai 2 in i o = ( v 0 )/ o = ( Ai 2 in )/ o in o i o i out v o Z out = /i out = o ( 2 in )/[o 2 in (A1)] o /(A1) since in >> 2, o o = open loop output impedance In general Z out = o /(1Ab) if voltage is sampled at output b = feedback fraction Z out = o (1Ab) if current is sampled at output g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 7

Comparators Frequently need to compare a signal with a reference eg temperature control, light detection, DVM, basis of analogue to digital conversion > 1 bit Comparator NB high gain differential amplifier, difference between inputs sends output to saturation ( or ) could be opamp without feedback or purpose designed IC Sometimes ICs designed with opencollector output so add pullup to supply also available with latch (memory) function v in Vref 2 V 1 V S V S no negative feedback so v v saturation voltages may not reach supply voltages check specs speed of transition Potential problem multiple transitions as signal changes near threshold g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 8

Hysteresis Add positive feedback (Schmitt trigger) V ref changes as > V S ie threshold falls once transition is made preventing immediate fall positive feedback speeds transition = A(V ref v ) V ref > v => = V s V ref = V high v in V ref 2 V 1 3 V S V S V ref < v => = 0V V ref = V low here, signal => logical "1": = 0V Output depends on history eg V = 10V, V S = 5V, 0V V high V low 1 = 10kΩ, 2 = 10kΩ, 3 = 100kΩ V out = 0V, V ref = 4.76V V out = 5V, V ref = 5V V S 0V hysteresis = V ref = 0.24V g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 9

Example alarm f 10V I photo V ref 1 4 2 3 0V g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 10

Oscillators Basic building block of many systems clock or timer, signal generators, function generators,... can exploit positive feedback elaxation oscillator charge capacitor C through ~exp(t/c) v crosses threshold at V ref, V out => ±V S V ref changes sign etc, etc square wave output: [V S,V S ] Period T = 2.2C C V S 1 V S 1 many more types of oscillator design available IC classic = 555 (many versions) external components set period and duty cycle g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 11

Wien bridge oscillator Sine wave oscillators also often required favourite circuit for audio test applications: low harmonic distortion at f ~ few khz r Gain = real at ω 0 = 1/C so positive feedback Lamp provides temperature dependent resistor C C G = /v = 3 at ωτ = 1 so negative feedback controls amplitude What values to choose for lamp resistance and r? Z 2 r What determines amount of harmonic distortion? Z 1 lamp g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 12

Temperature controller A frequent requirement similar to many other control applications eg cryostat with stable temperature maintained by resistive heater, or oven, OnOff control T < T 0 set heater to maximum power simulation add hysteresis (T 01, T 02 ) to prevent noise from switching too rapidly ok for central heating or domestic oven but not good for stable measurements try to improve g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 13

P & PD Temperature control Set heater power, proportional to temperature difference (P) W = P(T meas T 0 ) T still oscillates and undershoots desired value unstable if heat too fast Add control term proportional to rate of change (PD) W = P[(T meas T 0 ) Dd(T meas T 0 )/dt] D too large: overshoot & ringing D too small: slow response g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 14

PID Temperature control PD can eliminate ringing & overshoot but undershoot error remains add integral term PID control W = P[(T meas T 0 ) Dd(T meas T 0 )/dt I (T meas T 0 ) dt] good results but need to choose coefficients P, D, I empirically to ensure stability we'll later look at methods to solve such system equations using transforms g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 15

Notes Temperature control circuit 1 >> 2 to avoid loading still need heating circuit want W α V out Diode ensures W 0 V diode? Time constants to be selected depend on appliance chosen commercial devices will recommend values Need to consider offset currents and voltages null, or consider more complex circuit design g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 16

Instrumentation amplifier High gain, dccoupled differential amplifier single ended output high input impedance high CM use to amplify small differential signals where large CM signal may be present but small normal mode eg strain gauge, other bridge circuits "weak" voltage source Drawback of differential amplifier relatively low input impedance CM relies on excellent resistor matching cheap opamps may have CM ~80dB 10V V V 5V V V ~ mv To measure 5mV signal with 1% error CM = 0.05/5000 = 100dB g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 17

Improved differential amplifier Add voltage buffers and choose precise resistors improves input impedance 0.1% resistors available careful nulling of circuits still need high CM from output amplifier big demands on precision v 1 1 v 2 1 2 2 often find restrictions on driving circuit ie source g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 18

Classic instrumentation amplifier Input stage differential gain v 10 v 1 = i 2 = v 2 v 20 (1) i 1 = v 1 v 2 v 1 v 10 2 (v 10 v 20 ) (v 1 v 2 ) = 2i 2 (v 10 v 20 ) = 2i 2 i 1 i 1 = (v 1 v 2 )(2 2 1 )/ 1 2 G diff = 1 2 2 / 1 Input stage common mode gain v 2 v 20 v 1 = v CM u 1 v 2 = v CM u 2 2v CM = v 1 v 2 with signal u 1 = u 2 = 0 educe requirements on second stage From (1) v 10 v 20 = v 1 v 2 still choose input amps for good CM G CM = 1 and null carefully emainder is normal differential amplifier, (G = 1 in this case) Instrumentation ICs available G diff = 1 2 2 / 1 G CM = 1 G diff = 1 G CM = 0 g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 19

The Instrumentation Amplifier in practice Can add some more useful features feed common mode level back as guard connect to cable shield reduce effects of cable capacitance, leakage currents sense voltage at load allows feedback to correct for losses in wiring or offset of DC conditions guard v 1 v 2 2 1 2 3 4 3 4 sense output reference Load G = (12 2 / 1 ) 4 / 3 g.hall@ic.ac.uk http://www.hep.ph.ic.ac.uk/instrumentation/ 20