COMSATS Institute of Information Technology Virtual campus Islamabad
COMSATS Institute of Information Technology Virtual campus Islamabad Dr. Nasim Zafar Electronics 1 - EEE 231 Fall Semester – 2012
The BJT Internal Capacitance and High Frequency Model • Nasim Zafar 2
Lecture No. 26 Reference: The BJT Internal Capacitance and High-Frequency Model Chapter-5. 8 Microelectronic Circuits Adel S. Sedra and Kenneth C. Smith. Nasim Zafar 3
The BJT Internal Capacitances Nasim Zafar 4
Introduction Ø So far, we have assumed transistor action to be instantaneous. Ø The models we have developed, do not include any elements like capacitors or inductors, that would cause time or frequency dependence. Nasim Zafar 5
Introduction Ø Actual transistors, however, exhibit charge storage phenomena that limit the speed and frequency of their operation. Ø In this lecture, we study the charge-storage effects that take place in the BJT Ø and take them into account by adding capacitances to the hybrid-π model. Nasim Zafar 6
BJT: Small Signal Model We now again, define some quantities: Nasim Zafar 7
BJT: Small Signal Model So The output resistance is:
High-Frequency BJT Model Nasim Zafar 9
High-Frequency BJT Model Ø The BJT inherently has junction capacitances which affect its performance at high frequencies. Cb represents the base charge. Collector Junction: depletion capacitance, Cμ Emitter Junction: depletion capacitance, Cje, and also diffusion capacitance, Cb. Nasim Zafar 10
BJT High-Frequency BJT Model (cont’d) v In an integrated circuit, the BJTs are fabricated in the surface region of a Si wafer substrate; another junction exists between the collector and substrate, resulting in substrate junction capacitance, CCS. BJT Cross-Section BJT Small-Signal Model
The PN Junction Capacitance Ø The following expressions apply for a PN junction diode: How do we apply this to BJTs? Nasim Zafar 12
The Base-Charging or Diffusion Capacitance Cde Ø When the transistor is operating in the active or saturation mode, minority-carrier charge, Qn , is stored in the base region. Ø We can express Qn in terms of the collector current i. C as Nasim Zafar 13
The Base-Charging or Diffusion Capacitance Ø Diffusion capacitance almost entirely exists in the forwardbiased pn junction. Ø For small signals we can define the small-signal diffusion capacitance Cde, Ø Expression of the small-signal diffusion capacitance Nasim Zafar 14
Junction Capacitances Ø The Base-Emitter Junction Capacitance CJE • The base-emitter junction or depletion layer capacitance Cje can be expressed as: • where Cje 0 is the value of Cje at zero voltage, V 0 e is the EBJ built-in voltage (typically, 0. 9 V), and m is the grading coefficient of the EBJ junction (typically, 0. 5). Nasim Zafar 15
Junction Capacitances Ø The Collector-Base junction Capacitance Cμ, • In active-mode operation, the CBJ is reverse biased, and its junction or depletion capacitance, usually denoted Cμ, can be found from where Cμ 0 is the value of Cμ at zero voltage, V 0 c is the CBJ built-in voltage (typically, 0. 75 V), and m is its grading coefficient (typically, 0. 2– 0. 5). Nasim Zafar 16
Junction Capacitances v Collector Junction: depletion capacitance, Cμ v Emitter Junction: depletion capacitance, Cπ and Nasim Zafar 17
Nasim Zafar 18
Ø The hybrid-π model of the BJT, including capacitive effects, is shown in Slide 20. Ø Specifically, there are two capacitances: Ø the emitter–base capacitance Cπ = Cb + Cje Ø and the collector–base capacitance Cμ. Ø Typically, Cπ is in the range of a few picofarads to a few tens of picofarads, Cμ is in the range of a fraction of a picofarad to a few picofarads. Nasim Zafar 19
The High-Frequency Hybrid- Model v Two capacitances Cπ and Cμ , where v One resistance rx. Accurate value is obtained form high frequency measurement. Nasim Zafar 20
The Cutoff and Unity-Gain Frequency: f. T Ø The “cut-off” frequency, f. T, is a measure of the intrinsic speed of a transistor, and is defined as the frequency when the common-emitter current gain falls to 1. Ø Sometime this is referred to as the transition frequency, or unity-current-gain frequency. Ø This is the most important parameter for a MODERN BJT Nasim Zafar 21
The Cutoff Frequency Ø The transistor data sheets do not usually specify the value of Cπ. Ø Rather, the behavior of β or hfe versus frequency is normally given. Ø In order to determine Cπ and Cμ we shall derive an expression for hfe, the CE short-circuit current gain, as a function of frequency in terms of the hybrid-π components. Ø For this purpose consider the circuit shown in slide 24, in which the collector is shorted to the emitter. Nasim Zafar 22
Transit Frequency, f. T v Conceptual Set-up to measure f. T
The Cutoff and Unity-Gain Frequency Ø Circuit for deriving an expression for Ø According to the definition, output port is short circuit. Nasim Zafar 24
The Cutoff Frequency Ø A node equation at C provides the short-circuit collector current Ic. Ic = (gm – s. Cμ )Vπ Nasim Zafar 25
The Cutoff and Unity-Gain Frequency (cont’d) Ø Expression of the short-circuit current transfer function Ø Characteristic is similar to the one of first-order low-pass filter Nasim Zafar 26
The Cutoff and Unity-Gain Frequency (cont’d) Ø Slide 28 shows a Bode plot for hfe. Ø From the – 6 -d. B/octave slope it follows that the frequency at which hfe drops to unity, which is called the unity-gain bandwidth ωT, is given by: ωT = β 0ωβ Nasim Zafar 27
The Cutoff and Unity-Gain Frequency (cont’d) Nasim Zafar 28
The Cutoff and Unity-Gain Frequency (cont’d) Nasim Zafar 29
The Cutoff and Unity-Gain Frequency (cont’d) v Typically, f. T is in the range of : v 100 MHz to tens of GHz. Nasim Zafar 30
Maximum Oscillation Frequency (fmax). Ø One final important figure of merit is the MAXIMUM OSCILLATION FREQUENCY (fmax). Ø Frequency at which unilateral power gain becomes 1. Nasim Zafar 31
Frequency Response of the CE Amplifier Nasim Zafar 32
High Frequency “Roll-Off” in Av Ø Typically, an amplifier is designed to work over a limited range of frequencies. – At “high frequencies”, the gain of an amplifier decreases. Nasim Zafar 33
Frequency Response of a CE Amplifier v The voltage gain of an amplifier is typically flat over the midfrequency range, but drops drastically for low or high frequencies. A typical frequency response is shown below. Nasim Zafar 34
Frequency Response of a CE Amplifier Av Roll-Off due to CL v High Frequency Band: A capacitive load (CL) causes the gain to decrease at high frequencies. – The impedance of CL decreases at high frequencies, so that it shunts some of the output current to ground. Nasim Zafar 35
Frequency Response of a CE Amplifier (contd. ) v Low Frequency Band: At low frequencies, the capacitor is effectively an open circuit, and Av vs. ω is flat. At high frequencies, the impedance of the capacitor decreases and hence the gain decreases. The “breakpoint” frequency is 1/(RCCL).
The Common-Emitter Amplifier Nasim Zafar 37
Frequency Response of a CE Amplifier Nasim Zafar 38
Frequency Response of a CE Amplifier v Low frequency Band: Ø For a Common-Emitter BJT: gain falls off due to the effects of capacitors CC 1, CC 2, and CE. v High-frequency Band: Ø is due to device capacitances Cπ and Cμ (combined to form Ctotal). Nasim Zafar 39
Frequency Response of a CE Amplifier (contd. ) Ø Each capacitor forms a break point (simple pole or zero) with a break frequency of the form f=1/(2πREq. C), where REq is the resistance seen by the capacitor. Ø CE usually yields the highest low-frequency break which establishes f. Low. Nasim Zafar 40
Amplifier Figure of Merit (FOM) v The gain-bandwidth product is commonly used to benchmark amplifiers. – We wish to maximize both the gain and the bandwidth. v Power consumption is also an important attribute. – We wish to minimize the power consumption. Operation at low T, low VCC, and with small CL superior FOM Nasim Zafar 41
- Slides: 41