title: Field-effect tetrode
text: # Field-effect tetrode
  
  The tetrode field-effect transistor or field-effect tetrode is a solid-state semiconductor device, constructed by creating two field-effect channels back-to-back, with a junction between. It is a four-terminal device which does not have specific gate terminals because each channel is a gate for the other, the voltage conditions modulating the current carried by the other channel.
  
  ## Current–voltage relationship
  
  Where the voltage on the first channel is $V_{1}-V_{2}$ and the voltage on the second channel is $V_{3}-V_{4}$, the current in the first channel, $I_{1}$, and the current in the second channel, $I_{2}$, are given by:
  
  $I_{1}=G_{1}(V_{1}-V_{2})\left[1-{\frac {2}{3V_{p}^{1/2}}}{\frac {(V_{1}-V_{3})^{(3/2)}-(V_{2}-V_{4})^{(3/2)}}{(V_{1}-V_{3})-(V_{2}-V_{4})}}\right]$
  
  and
  
  $I_{2}=G_{2}(V_{3}-V_{4})\left[1-{\frac {2}{3V_{p}^{1/2}}}{\frac {(V_{3}-V_{1})^{(3/2)}-(V_{4}-V_{2})^{(3/2)}}{(V_{3}-V_{1})-(V_{4}-V_{2})}}\right]$,
  
  where the $G_{i}$ are the low-voltage conductance of the channels and $V_{p}$ is the pinch-off voltage (assumed to be the same for each channel).
  
  ## Applications
  
  The field-effect tetrode can be used as a highly linear electronically variable resistor – resistance is not modulated by signal voltage. Signal voltage can exceed bias voltage, pinch-off voltage, and junction breakdown voltage. The limit is dependent on dissipation. Signal current flows in inverse proportion to the channel resistances. The signal does not modulate the depletion layer, so the tetrode can perform at high frequencies. The tuning ratio can be very large – the high resistance limit is in the megohms range for symmetrical pinch-off conditions.
  
  