EEE 194RF Simple BJT Amps: High Frequency 1 HIGH-FREQUENCY RESPONSE OF SIMPLE BJT AMPLIFIERS At high frequencies, the amplifier response is characterized by midband and high-frequency poles. Single BJT amplifiers are analyzed. Common-emitter amplifier high-frequency response • AC model of a simple BJT common-emitter amplifier is shown in Figure 1. RBRCQ1RSvovs++−−RBRCRSvovs+ +− −rogmvπrπrbvπ+−CπCµ(a)(b) Figure 1. Common-Emitter Equivalent Circuits (a) Midband AC Equivalent, (b) High-Frequency Equivalent • The input portion of the high-frequency equivalent circuit is simplified for analysis as shown in Figure 2. RCR'Svovi+ +− −rogmvπrπrbvπ+−CπCµRSRB=vSRS( )RSRB= Figure 2. Simplified Input Portion of High-Frequency Equivalent Circuit • Miller's Theorem is used to simplify the high-frequency equivalent circuit made complex by the presence of Cµ which interconnects the input and output sections of the circuit. • The two-port network accentuated by the shaded area has a midband voltage gain of ()'omo C mCvAgrRgRvπ==− =− , which is used in Miller's Theorem, 1211ZAZZZAA==−− . (10.5-2) General LinearNetworkV = A V2 1 21VVZ++−−ΙΙΙΙ1i 2iin outGeneral LinearNetworkV = A V2 1 21VV+−+−ZZ12ΙΙ ΙΙ1s 2sin outwithwith(a) (b) Figure 3. Miller's Equivalent Circuits : (a) Interconnecting Impedance, (b) Port-Shunting Impedance • The use of Miller's Theorem results in the following equivalent circuit:EEE 194RF Simple BJT Amps: High Frequency 2 RC vo+−ogmvπrπrbvπ+−Ci C'R'Svi+−RSRB=vSRS( )RSRB= Figure 4. Miller's Theorem Applied to a Common-Emitter Amplifier where ()()''111111imCimCjCCC gRjC AjC gRµµµωωω== ⇒ =+−−− and ()()''''1111mCmCoo mCmCAgRjCgRCCjC A gRjC gRµµµωωω+−== ⇒ =−−− • The voltage gain of the circuit is therefore: ''111oo iVSisSBimCoSSbivvvvAvvvvrRRjCgRjC RRr rjCππππωωω===−++ Simplifying this expression to yield an expression for the gain which clearly shows the poles of the amplifier: ()()()'''1111mCBVSBb Bb oCiSbgRRrARR r r Rr r jCRjCr R rππππωω−=++ + + +++ • The high frequency poles for the common-emitter amplifier as shown in Figure 1 are: 1'11PoCjCRωω=+ and ()2'11PiSbjCr R rπωω=++ . • Simply put, the voltage gain characteristics of the amplifier at high frequencies is composed of the midband voltage and the lowpass transfer characteristics of the input and output portions of the high-frequency equivalent circuit: []()''1111VVmoCiSbAAjCRjCr R rπωω=+++ . Common-collector amplifier high-frequency response • AC model of a simple BJT common-collector amplifier is shown in Figure 5.EEE 194RF Simple BJT Amps: High Frequency 3 RBRCQ1RSvovs++−−RBRCRSvovs++−−rogmvπrπrbvπ+−CπCµ(a)(b)RBRB Figure 5. Common-Collector Equivalent Circuits (a) Midband AC Equivalent, (b) High-Frequency Equivalent • The input portion of the high-frequency equivalent circuit is simplified for analysis as shown in Figure 6. For simplicity, ro is considered to be very large compared to RC and RE. RCvo++−−gmvπrπrbvπ+−CπCµRBR'SviRSRB=vSRS( )RSRB= Figure 6. Simplified Input Portion of High-Frequency Equivalent Circuit • The gain of the shaded two-port network is ()ecmC EvAgRRvπ==− + which is used in Miller's Theorem, 1211ZAZZZAA==−− . (10.5-2) • When Miller's Theorem is applied to the common-collector amplifier, ()1imCECCC gR Rπµ=+ + + and ()()1mC EOmC EgR RCC CgR Rµµ++=≈+ with the equivalent circuit shown in Figure 7: RCvo++−−gmvπrπrbvπ+−CιRBR'SviRSRE=vSRS( )RSRE=Cο Figure 7. Miller's Theorem Applied to a Common-Collector AmplifierEEE 194RF Simple BJT Amps: High Frequency 4 • The pole introduced by the Ci is of primary interest since Co is less than the input capacitance. Therefore, assume that the pole introduced by Co is sufficiently high so that Co can be replaced by an open circuit. • The voltage gain of the common-collector amplifier is: () ()''1omESVsSb mE i SbSvgrRRAvRr gRrjCrRrRπππω=≈+++ + + • The dominant high-frequency pole is (){}111111PSb SbimCEmE mERr RrCr C C g R R rgR gRππµ πω≈=  ++++ +  ++    . • Common-emitter amplifiers with emitter resistors have the same basic topology as the common-collector amplifier. The resultant pole location remains identical. Common-base amplifier high-frequency response • AC model of a simple BJT common-base amplifier is shown in Figure 8. RERCQ1RSvovs++−−RERCRSvovi++−−gmvπrπrbvπ+−CπCµ(a)(b)RBCBvsRERSRS=R 'S= Figure 8. Common-Base Equivalent Circuits (a) Midband AC Equivalent, (b) High-Frequency Equivalent • Note that there are no capacitors bridging the input and output terminals: therefore, there do not exist Miller effect high valued capacitors. Therefore, the poles are at very high frequencies. • To simplify the analysis, assume that the base current is small so the voltage across rb is also small. Then rb can be ignored: that is, let rb = 0 and ve ≈ −vπ. • The poles are located at ()()()11''mSEFPTSErgrRRCrCr R Rππππππβωω++=≈= and 21PCCRµω= . • Both poles are at very high frequencies. Therefore, common-base amplifiers are not usually the frequency limiting elements in a multistage