Chapter 5b Sensors and Detectors

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Contents

General Noise Model For Detector System

Effect of Parallel Load Resistance

Effect of Shunt Capacitance

Voltaic Sensor

Optoelectronic Detector

• A detector is typically the first stage of a communication system. Noise in this stage may have significant effects on the operation of the entire system. In this chapter we will use detector and sensor interchangeably.
• A detector or sensor senses a physical parameter of some kind. In the field of optics and infrared the term detector is typically used.
• To develop the noise model of a sensor, we can start with its circuit diagram. From this we draw an ac equivalent circuit that includes all impedances and generators. To each resistance and current generator we add the appropriate thermal noise an excess noise. The current generators may have shot noise, 1/f noise and burst noise. Using this equivalent circuit an expression for gain and equivalent input noise can be derived.
• A typical sensor/detector electronic system includes a coupling device or network as well as an amplifier. The noise equivalent circuit of the coupling network is easily obtained, and the E_n-I_n representation is valid for the amplifier. When we combine these three parts, we obtain a equivalent for the system.
• The derivation of the equivalent input noise for the system follows 3 steps:
  • Determine the total output noise.
  • Calculate the system gain.
  • Divide the total output noise by the system gain to obtain the equivalent input noise.

   

General Noise Model For Detector System

• In the diagram shown the sensor is described by its signal voltage V_s , its internal impedance Z_s, and a noise generator E_s which represents all sources of sensor noise. To generalize the diagram a coupling network represented by impedance Z_c and an noise source E_c is included in shunt with the input. We want to combine and reflect all noise sources to the input as shown in Fig. 5-1(b) and (c).
• A general form for the equivalent input noise voltage is



• Alternatively



• where



• If the signal source is a current generator, the equivalent noise current expression is more convenient. If the signal is a voltage generator, the equivalent is more convenient.

Effect of Parallel Load Resistance

• The simplest type of sensor is represented by a resistance in series with a signal voltage generator as shown in Fig. 5-2
• Also shown is a shunt network consisting of R_p and noise generator E_p. One practical purpose of the circuit may be to supply the sensor with bias power. The signal V_s and noise E_s of the sensor are in series with the source resistance. The input signal-to-noise power ratio is simply the ratio of V_s² to E_s². When a load resistor such as R_p or other coupling network elements are added, the output signal-to-noise ratio is degraded.
• Example: Determine the output signal-to-noise ratio when R_p=R_s
• Since E_s=E_p it follows that

  

• The output signal is Therefore, the output SNR is

  

• We conclude that a shunt resistor decreases the signal more than the noise and the result is a decrease in the SNR. For the matched condition, source resistance equal to the load resistance the SNR is reduced by 50%.
• For a more complete circuit as shown in Fig. 5-3
• Here a noisy shunt resistance is present. For convenience we represent its noise by a current generator . Amplifier noise E_n and I_n are added. We calculate the equivalent noise following the steps below:
• From the equivalent circuit determine the output noise E_no



• Calculate the system gain K_t the transfer function from sensor to output



• Divide the output noise by the system gain to obtain the equivalent input noise

  

Effect of Shunt Capacitance

• Although capacitance is virtually noise free, it can increase the equivalent input noise. A shunt capacitance does not affect the sensor SNR because it decreases the sensor signal and noise equally, but not the following amplifier noise. Consider the equivalent circuit shown and using the method outlined above the output noise is
• The gain of the system is

  

• Thus the equivalent input noise is

  

• Fig. 5-4

Voltaic Sensor

• As a first example we consider the case of a resistive sensor that generates a voltage signal. These detectors include the thermocouple, pyroelectric infrared cell, generators, and other primarily detectors that are resistive in nature that generate a voltage signal.
• A simple circuit diagram is shown in Fig. 5-5 and Fig. 5-6
• The sensor is represented by the signal source V_s and the internal series resistance R_s. The voltage V_s is the output from the sensed physical or electrical parameter such as pressure or radiation. A coupling capacitor C_c can be used if we are interested exclusively in the time-varying output of the sensor. The element R_L may be needed for impedance matching. The noise model of the sensor-amplifier system is shown in Fig. 8-2. The shunt capacitance C_p can be in the sensor assembly or it may represent the parasitic stray capacitance between lead wires. The amplifier is now represented by the noise parameters E_n and I_n.
• For low noise, the noise contribution of R_L is kept low if it is large. The shunt capacitance should be minimized to avoid increasing E_n at high frequencies. The decoupling capacitor C_c should be very large or removed to reduce its effect on the amplifier¡¦s In noise at low-frequencies. The amplifier input resistance R_i can often be reduced with overall negative feedback to increase the corner frequency caused by C_p

Optoelectronic Detector

• An optoelectronic detector is used to detect various forms of visible and nonvisible radiation and has a wide range of applications such as infrared detection, heat measurement, light and color measurement, fiber optic detectors, sensors for compact disk players, laser detectors and many other uses.
• There are 2 general types of solid-state photon detectors: photoconductive and photovoltaic.
• In a photoconductive detector, radiation on a cell produced a current in addition to the dark current. Bias is applied to the cell to collect the current. In a photovoltaic detector, radiation on the cell produces a voltage directly. Photoconductive cells can be fabricated from bulk semiconductor material where the conductivity increases as radiant energy is absorbed.
• The simplified circuit diagram is shown in Fig. 5-7
• The reverse bias is supplied by V_BB, which collects the current generated by the radiant photon signal. A voltage signal is developed across the load or bias resistor R_B.
• Most often photodiodes are used with op amps employing negative feedback to produce the photoconductive detector as shown in Fig. 5-8
• The feedback resistor R_B produces a virtual ground at the anode of the photodiode which reduces the input impedance, and thereby increasing the frequency response. The output voltage is V₀=-I_DR_B where I_D is the reverse bias current in the photodiode. Ideally, R₂=R_B to reduce the output
• offset voltage caused by the input bias current. However, R₂ adds noise as can be seen from the noise equivalent circuit below: The load resistor R_B has the same effect on equivalent input noise and gain for either circuit. The noise equivalent circuit of the photodiode detector is shown in Fig.8-7. The signal current source I_s is located at the input and :
• r_d = noiseless dynamic reverse-bias resistance of the photodiode
• R_B = feedback resistance
• R_cell = cell series resistance (< 50W)
• R₂ = bias resistor for noninverting input
• E_cell = thermal noise of Rcell
• E_n = amplifier noise voltage
• C_d = cell capacitance
• C_W = stray wiring capacitance
• I_D = sensor dc photocurrent plus dark current
• I_nB = (4kT/R_B)^1/2 = thermal noise of R_B
• I_p = (I_sh² +I_G-R² +I_1/f²)^1/2
• I_n1 = amplifier noise current for inverting input
• I_n2 = amplifier noise current for noninverting input
• I₂ = thermal noise current of R₂
• Fig. 5-9
• The cell capacitance C_d and wiring capacitance C_W probably will be the frequency-limiting elements so they should be kept as small as possible. The input capacitance, C_i, and input resistance, R_i, drop out of the noise expression, they do affect the amplifier gain. This gives us a mechanism for optimizing the frequency and noise responses separately.