Presentation on theme: "Frequency response I As the frequency of the processed signals increases, the effects of parasitic capacitance in (BJT/MOS) transistors start to manifest."— Presentation transcript:
1Frequency response IAs the frequency of the processed signals increases, the effects of parasitic capacitance in (BJT/MOS) transistors start to manifestThe gain of the amplifier circuits is frequency dependent, usually decrease with the frequency increase of the input signalsComputing by hand the exact frequency response of an amplifier circuits is a difficult and time-consuming task, therefore approximate techniques for obtaining the values of critical frequencies is desirableThe exact frequency response can be obtained from computer simulations (e.g SPICE). However, to optimize your circuit for maximum bandwidth and to keep it stable one needs analytical expressions of the circuit parameters or at least know which parameter affects the required specification and how
2Frequency response IIThe transfer function gives us the information about the behavior of a linear-time-invariant (LTI) circuit/system for a sinusoidal excitation with angular frequencyThis transfer function is nothing but the ratio between the Fourier transforms of the output and input signals and it is also called the frequency response of the LTI circuit.represents the gain magnitude of the frequency response of the circuit, whereas is the phase of frequency response. Often, it is more convenient to express gain magnitude in decibels.To amplify a signal without distortion, the amplifier gain magnitude must be the same for all of the frequency components
3Frequency response of amplifers A bode plot shows the the gain magnitude and phase in decibles versus frequency on logarithmic scaleA few prerequisites for bode plot:Laplace transform and network transfer functionPoles and zeros of transfer functionBreak frequenciesSome useful rules for drawing high-order bode plots:Decompose transfer function into first order terms.Mark the break frequencies and represent them on the frequency axis the critical values for changesMake bode plot for each of the first order termFor each first order term, keep the DC to the break frequency constant equal to the gain at DCAfter the break frequency, the gain magnitude starts to increase or decrease with a slope of 20db/decade if the term is in the numerator or denominatorFor phase plot, each first order term induces a 45 degrees of increase or decrease at the break frequency if the term is in the numerator or denominatorConsider frequencies like one-tenth and ten times the break frequency and approximate the phase by 0 and 90 degrees if the frequency is with the numerator (or 0 and -90 degrees if in the denominator)Add all the first order terms for magnitude and phase response
4Frequency response of RLC circuits E.g. 1E.g. 2E.g. 3
9Frequency response of common source MOS amplifer High-frequency MOS Small-signalequivalent circuitMOSFET common Source amplifierSmall-signal equivalent circuit for the MOS common source amplifierFrequency response analysis shows that there are three break frequencies, and mainly the lowest one determines the upper half-power frequency, thus the -3db bandwidth
10Exact frequency response of amplifiers Exact frequency analysis of amplifier circuits is possible following the steps:Draw small-signal equivalent circuit (replace each component in the amplifier with its small-signal circuit)Write equations using voltage and current lawsFind the voltage gain as a ratio of polynomial of laplace variable sFactor numerator and denominator of the polynomial to determine break frequenciesDraw bode plot to approximate the frequency response
11Graphs from Prentice Hall The Miller EffectConsider the situation that an impedance is connected between input and output of an amplifierThe same current flows from (out) the top input terminal if an impedance is connected across the input terminalsThe same current flows to (in) the top output terminal if an impedance is connected across the output terminalThis is know as Miller EffectTwo important notes to apply Miller Effect:There should be a common terminal for input and outputThe gain in the Miller Effect is the gain after connecting feedback impedanceGraphs from Prentice Hall
12Application of Miller Effect If the voltage gain magnitude is large (say larger than 10) compared to unity,thenwe can perform an approximate analysis by assuming is equal tofind the gain including loading effects ofuse the gain to find outThus, using Miller Effect, gain calculation and frequency response characterization would be much simpler
13Application of Miller Effect If the feedback impedance is a capacitor ,then the Miller capacitance reflected across the input terminal isTherefore, connecting a capacitance from the input to output is equivalent to connecting a capacitanceDue to Miller effect, a small feedback capacitance appears across the input terminals as a much larger equivalent capacitance with a large gain (e.g ). At high frequencies, this large capacitance has a low impedance that tends to short out the input signal
14The model for low-frequency analysis BJT small-signal models (for BJT amplifiers)The model for low-frequency analysisThe model for high-frequency analysisThe base-spreading resistance for the base region (very small)The dynamic resistance of the base emitter regionThe feedback resistance from collector to base (very large)Account for the upward slope of the output characteristicThe depletion capacitance of the collector-to-base regionThe diffusion capacitance of the base-to-emitter junctionNote: in the following analysis of the CE, EF and CB amplifier in the next three slides, we will assume for simplicity (though they still appear in the small signal models).
16Miller Effect: common emitter amplifier II Assume the current flowing through is very small compared to , then the gain will be considering the input terminal of the amplifier at b’ to ground.Applying the miller effect for the amplifier, the following simplified circuit can be obtained:Thus, the total capacitance from terminal b’ to ground is given as follows (neglect the miller capacitance from output terminal c to ground):The break frequency, thus the -3db frequency is set by the RC lowpass filter (other voltage controlled current source, resistance does not contribute to the break frequency) is a main limiting factor for -3db bandwidth.
17Emitter-follower amplifier Using Miller Effect, we obtain the above equivalent circuit. If neglecting , It shows that the break frequency is
18Common base amplifierWhat about amplifier that do not have capacitance connected directly from output to the input?For approximate analysis, we can neglect the simplified equivalent circuit can be shown in (c). Derive the transfer function for this circuit, it shows two break frequencies (with typical values, is approximately -3db bandwidth)
19Fully-differential amplifier XXTo estimate the 3dB bandwidth of this one, note that the circuit if fully symmetric, so only the half circuit needs to be analyzed. The node voltage at X is 0 in small-signal analysis. Therefore we only need to analyze the right-hand side circuit, which is actually a common-emitter amplifier analyzed before. So the 3dB bandwidth of a common-emitter amplifier applies here.
20Graphs from Prentice Hall Cascode amplifier and differential amplifierThe cascode amplifier can be viewed as a common-emitter amplifier with a common-base amplifier.Due to low input impedance of Q2, the voltage gain of Q1 is small. So, Miller effect on Q1 is small.The Emitter-coupled differential amplifier can be viewed as a emitter-follower amplifier cascaded with a common-base amplifier (both have wider bandwidth than common-emitter amplifier).Graphs from Prentice Hall