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Common collector
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<h2 id="basic-circuit">Basic circuit</h2> <p>The circuit can be explained by viewing the transistor as being under the control of <a href="/facts/Negative_feedback/G9byVgpN">negative feedback</a>. From this viewpoint, a common-collector stage (Fig. 1) is an <a href="/facts/Negative-feedback_amplifier/zQSRBReJ">amplifier with full series negative feedback</a>. In this configuration (Fig. 2 with β = 1), the entire output <a href="/facts/Voltage/EN2po6N2">voltage</a> <i>V</i>out is placed contrary and <a href="/facts/In_series/007qC7j8">in series</a> with the input voltage <i>V</i>in. Thus the two voltages are subtracted according to <a href="/facts/Kirchhoff%2527s_voltage_law/fGAAFXB3">Kirchhoff's voltage law</a> (KVL) (the subtractor from the function block diagram is implemented just by the input loop), and their difference <i>V</i>diff = <i>V</i>in − <i>V</i>out is applied to the base–emitter junction. The transistor continuously monitors <i>V</i>diff and adjusts its emitter voltage to equal <i>V</i>in minus the mostly constant <i>V</i>BE (approximately one <a href="/facts/Diode/JyaoyGnk">diode forward voltage drop</a>) by passing the collector <a href="/facts/Electric_current/Dc1xdnUX">current</a> through the emitter <a href="/facts/Resistor/JrsGReM6">resistor</a> RE. As a result, the output voltage <i>follows</i> the input voltage variations from <i>V</i>BE up to <i>V</i>+; hence the name "emitter follower". </p><p>Intuitively, this behavior can be also understood by realizing that <i>V</i>BE is very insensitive to <a href="/facts/Biasing/lK0e6hbK">bias</a> changes, so any change in base voltage is transmitted (to good approximation) directly to the emitter. It depends slightly on various disturbances (transistor <a href="/facts/Engineering_tolerance/zRrj34dF">tolerances</a>, <a href="/facts/Temperature/QyGe4gmj">temperature</a> variations, load resistance, a collector resistor if it is added, etc.), since the transistor reacts to these disturbances and restores the equilibrium. It never saturates even if the input voltage reaches the positive rail. </p><p>The common-collector circuit can be shown mathematically to have a <a href="/facts/Gain_(electronics)/CWbehg27">voltage gain</a> of almost unity: </p> A v = v out v in ≈ 1. {\displaystyle A_{v}={\frac {v_{\text{out}}}{v_{\text{in}}}}\approx 1.} <p>A small voltage change on the input terminal will be replicated at the output (depending slightly on the transistor's gain and the value of the load resistance; see gain formula below). This circuit is useful because it has a large <a href="/facts/Input_impedance/AQCLaTj9">input impedance</a> </p> r in ≈ β 0 R E , {\displaystyle r_{\text{in}}\approx \beta _{0}R_{\text{E}},} <p>so it will not load down the previous circuit, and a small <a href="/facts/Output_impedance/80brK3Cv">output impedance</a> </p> r out ≈ R E ∥ R source β 0 , {\displaystyle r_{\text{out}}\approx {\frac {R_{\text{E}}\parallel R_{\text{source}}}{\beta _{0}}},} <p>so it can drive low-resistance <a href="/facts/Electrical_load/IX0XBAqB">loads</a>. </p><p>Typically, the emitter resistor is significantly larger and can be removed from the equation: </p> r out ≈ R source β 0 . {\displaystyle r_{\text{out}}\approx {\frac {R_{\text{source}}}{\beta _{0}}}.} <h2 id="applications">Applications</h2> <p>The common collector amplifier's low output impedance allows a source with a large <a href="/facts/Output_impedance/80brK3Cv">output impedance</a> to drive a small <a href="/facts/Load_impedance/AQCLaTj9">load impedance</a> without changing its voltage. Thus this circuit finds applications as a voltage <a href="/facts/Buffer_amplifier/KLM5GzpF">buffer</a>. In other words, the circuit has current gain (which depends largely on the <i>h</i>FE of the transistor) instead of voltage gain. A small change to the input current results in much larger change in the output current supplied to the output load. </p><p>One aspect of buffer action is transformation of impedances. For example, the <a href="/facts/Th%25C3%25A9venin%2527s_theorem/rwYa905x">Thévenin resistance</a> of a combination of a voltage follower driven by a voltage source with high Thévenin resistance is reduced to only the output resistance of the voltage follower (a small resistance). That resistance reduction makes the combination a more ideal voltage source. Conversely, a voltage follower inserted between a small load resistance and a driving stage presents a large load to the driving stage—an advantage in coupling a voltage signal to a small load. </p><p>This configuration is commonly used in the output stages of <a href="/facts/Power_amplifier_classes/ocDIVQ73">class-B</a> and <a href="/facts/Power_amplifier_classes/ocDIVQ73">class-AB</a> amplifiers. The base circuit is modified to operate the transistor in class-B or AB mode. In <a href="/facts/Power_amplifier_classes/ocDIVQ73">class-A</a> mode, sometimes an active <a href="/facts/Current_source/1UkYH0aG">current source</a> is used instead of <i>R</i>E (Fig. 4) to improve linearity and/or efficiency.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> </p> <h2 id="characteristics">Characteristics</h2> <p>At low frequencies and using a simplified <a href="/facts/Hybrid-pi_model/VwzM3JAk">hybrid-pi model</a>, the following <a href="/facts/Small-signal_model/P3VYrx4K">small-signal</a> characteristics can be derived. (Parameter β = g m r π {\displaystyle \beta =g_{m}r_{\pi }} and the <a href="/facts/Parallel_(geometry)/16r5yq7D">parallel</a> lines indicate <a href="/facts/Series_and_parallel_circuits/007qC7j8">components in parallel</a>.) </p> <table><tbody><tr><th></th><th>Definition</th><th>Expression</th><th>Approximate expression</th><th>Conditions</th></tr><tr><th><a href="/facts/Gain_(electronics)/CWbehg27">Current gain</a></th><td> A i = i out i in {\displaystyle A_{\mathrm {i} }={i_{\text{out}} \over i_{\text{in}}}} </td><td> β 0 + 1 {\displaystyle \beta _{0}+1\ } </td><td> ≈ β 0 {\displaystyle \approx \beta _{0}} </td><td> β 0 ≫ 1 {\displaystyle \beta _{0}\gg 1} </td></tr><tr><th><a href="/facts/Gain_(electronics)/CWbehg27">Voltage gain</a></th><td> A v = v out v in {\displaystyle A_{\mathrm {v} }={v_{\text{out}} \over v_{\text{in}}}} </td><td> g m R E g m R E + 1 {\displaystyle {g_{m}R_{\text{E}} \over g_{m}R_{\text{E}}+1}} </td><td> ≈ 1 {\displaystyle \approx 1} </td><td> g m R E ≫ 1 {\displaystyle g_{m}R_{\text{E}}\gg 1} </td></tr><tr><th><a href="/facts/Input_resistance/AQCLaTj9">Input resistance</a></th><td> r in = v in i in {\displaystyle r_{\text{in}}={\frac {v_{\text{in}}}{i_{\text{in}}}}} </td><td> r π + ( β 0 + 1 ) R E {\displaystyle r_{\pi }+(\beta _{0}+1)R_{\text{E}}\ } </td><td> ≈ β 0 R E {\displaystyle \approx \beta _{0}R_{\text{E}}} </td><td> ( g m R E ≫ 1 ) ∧ ( β 0 ≫ 1 ) {\displaystyle (g_{m}R_{\text{E}}\gg 1)\wedge (\beta _{0}\gg 1)} </td></tr><tr><th><a href="/facts/Output_resistance/80brK3Cv">Output resistance</a></th><td> r out = v out i out {\displaystyle r_{\text{out}}={\frac {v_{\text{out}}}{i_{\text{out}}}}} </td><td> R E ∥ r π + R source β 0 + 1 {\displaystyle R_{\text{E}}\parallel {r_{\pi }+R_{\text{source}} \over \beta _{0}+1}} </td><td> ≈ 1 g m + R source β 0 {\displaystyle \approx {1 \over g_{m}}+{R_{\text{source}} \over \beta _{0}}} </td><td> ( β 0 ≫ 1 ) ∧ ( r in ≫ R source ) {\displaystyle (\beta _{0}\gg 1)\wedge (r_{\text{in}}\gg R_{\text{source}})} </td></tr></tbody></table> <p>Where R source {\displaystyle R_{\text{source}}\ } is the <a href="/facts/Th%25C3%25A9venin%2527s_theorem/rwYa905x">Thévenin</a> equivalent source resistance. </p> <h3>Derivations</h3> <p>Figure 5 shows a low-frequency hybrid-pi model for the circuit of Figure 3. Using <a href="/facts/Ohm%2527s_law/PjfEyTgI">Ohm's law</a>, various currents have been determined, and these results are shown on the diagram. Applying Kirchhoff's current law at the emitter one finds: </p> ( β + 1 ) v in − v out R S + r π = v out ( 1 R L + 1 r O ) . {\displaystyle (\beta +1){\frac {v_{\text{in}}-v_{\text{out}}}{R_{\text{S}}+r_{\pi }}}=v_{\text{out}}\left({\frac {1}{R_{\text{L}}}}+{\frac {1}{r_{\text{O}}}}\right).} <p>Define the following resistance values: </p> 1 R E = 1 R L + 1 r O , R = R S + r π β + 1 . {\displaystyle {\begin{aligned}{\frac {1}{R_{\text{E}}}}&={\frac {1}{R_{\text{L}}}}+{\frac {1}{r_{\text{O}}}},\\[2pt]R&={\frac {R_{\text{S}}+r_{\pi }}{\beta +1}}.\end{aligned}}} <p>Then collecting terms the voltage gain is found: </p> A v = v out v in = 1 1 + R R E . {\displaystyle A_{\text{v}}={\frac {v_{\text{out}}}{v_{\text{in}}}}={\frac {1}{1+{\frac {R}{R_{\text{E}}}}}}.} <p>From this result, the gain approaches unity (as expected for a <a href="/facts/Buffer_amplifier/KLM5GzpF">buffer amplifier</a>) if the resistance ratio in the denominator is small. This ratio decreases with larger values of current gain β and with larger values of R E {\displaystyle R_{\text{E}}} . The input resistance is found as </p> R in = v in i b = R S + r π 1 − A v = ( R S + r π ) ( 1 + R E R ) = R S + r π + ( β + 1 ) R E . {\displaystyle {\begin{aligned}R_{\text{in}}&={\frac {v_{\text{in}}}{i_{\text{b}}}}={\frac {R_{\text{S}}+r_{\pi }}{1-A_{\text{v}}}}\\&=\left(R_{\text{S}}+r_{\pi }\right)\left(1+{\frac {R_{\text{E}}}{R}}\right)\\&=R_{\text{S}}+r_{\pi }+(\beta +1)R_{\text{E}}.\end{aligned}}} <p>The transistor output resistance r O {\displaystyle r_{\text{O}}} ordinarily is large compared to the load R L {\displaystyle R_{\text{L}}} , and therefore R L {\displaystyle R_{\text{L}}} dominates R E {\displaystyle R_{\text{E}}} . From this result, the input resistance of the amplifier is much larger than the output load resistance R L {\displaystyle R_{\text{L}}} for large current gain β {\displaystyle \beta } . That is, placing the amplifier between the load and the source presents a larger (high-resistive) load to the source than direct coupling to R L {\displaystyle R_{\text{L}}} , which results in less signal attenuation in the source impedance R S {\displaystyle R_{\text{S}}} as a consequence of <a href="/facts/Voltage_division/PYYlGlYU">voltage division</a>. </p><p>Figure 6 shows the small-signal circuit of Figure 5 with the input short-circuited and a test current placed at its output. The output resistance is found using this circuit as </p> R out = v x i x . {\displaystyle R_{\text{out}}={\frac {v_{\text{x}}}{i_{\text{x}}}}.} <p>Using Ohm's law, various currents have been found, as indicated on the diagram. Collecting the terms for the base current, the base current is found as </p> ( β + 1 ) i b = i x − v x R E , {\displaystyle (\beta +1)i_{\text{b}}=i_{\text{x}}-{\frac {v_{\text{x}}}{R_{\text{E}}}},} <p>where R E {\displaystyle R_{\text{E}}} is defined above. Using this value for base current, Ohm's law provides </p> v x = i b ( R S + r π ) . {\displaystyle v_{\text{x}}=i_{\text{b}}\left(R_{\text{S}}+r_{\pi }\right).} <p>Substituting for the base current, and collecting terms, </p> R out = v x i x = R ∥ R E , {\displaystyle R_{\text{out}}={\frac {v_{\text{x}}}{i_{\text{x}}}}=R\parallel R_{\text{E}},} <p>where || denotes a parallel connection, and R {\displaystyle R} is defined above. Because R {\displaystyle R} generally is a small resistance when the current gain β {\displaystyle \beta } is large, R {\displaystyle R} dominates the output impedance, which therefore also is small. A small output impedance means that the series combination of the original voltage source and the voltage follower presents a <a href="/facts/Th%25C3%25A9venin%2527s_theorem/rwYa905x">Thévenin voltage source</a> with a lower Thévenin resistance at its output node; that is, the combination of voltage source with voltage follower makes a more ideal voltage source than the original one. </p> <h2 id="see-also">See also</h2> <ul> <li>Electronics portal</li></ul> <ul><li><a href="/facts/Common_base/KK7aHT5e">Common base</a></li> <li><a href="/facts/Common_emitter/GBVl6DPa">Common emitter</a></li> <li><a href="/facts/Common_gate/I6fF7PaU">Common gate</a></li> <li><a href="/facts/Common_drain/fJRvThwB">Common drain</a></li> <li><a href="/facts/Common_source/8UDNcIpv">Common source</a></li> <li><a href="/facts/IC_power-supply_pin/moPAAjnl">IC power-supply pin</a></li> <li><a href="/facts/Open_collector/E12DL8fL">Open collector</a></li> <li><a href="/facts/Two-port_network/cqUrBTYq">Two-port network</a></li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://web.archive.org/web/20070909222435/http://people.seas.harvard.edu/~jones/es154/lectures/lecture_3/bjt_amps/bjt_amps.html">R Victor Jones: <i>Basic BJT Amplifier Configurations</i></a></li> <li><a href="http://230nsc1.phy-astr.gsu.edu/hbase/electronic/npncc.html">NPN Common Collector Amplifier</a> — <a href="/facts/HyperPhysics/KWfaNNm8">HyperPhysics</a></li> <li><a href="http://www.tedpavlic.com/teaching/osu/ece327/lab1_bjt/lab1_bjt_transistor_basics.pdf">Theodore Pavlic: ECE 327: Transistor Basics; part 6: <i>npn Emitter Follower</i></a></li> <li><a href="https://web.archive.org/web/20050405185240/http://www.phys.ualberta.ca/~gingrich/phys395/notes/node86.html">Doug Gingrich: <i>The common collector amplifier</i> U of Alberta </a></li> <li><a href="/facts/Raymond_E._Frey_(physicist)/TquqI3wa">Raymond Frey</a><a href="https://web.archive.org/web/20060919004917/http://zebu.uoregon.edu/~rayfrey/431/lab3_431.pdf">: <i>Lab exercises</i> U of Oregon</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Rod Elliot: 20 Watt Class-A Power Amplifier <a href="https://sound-au.com/project10.htm" target="_blank">https://sound-au.com/project10.htm</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> </ol>