AD8011 This analysis assumes perfect current sources and infinite transistor VAs (Q3, Q4 output conductances are assumed zero). These assumptions result in actual vs. model open loop voltage gain and associated input referred error terms being less accurate for low gain (G) noninverting operation at the frequencies below the open loop pole of the AD8011. This is primarily a result of the input signal (VP) modulating the output conductances of Q3/Q4 resulting in RI less negative than derived here. For inverting operation, the actual vs. model dc error terms are relatively much less.
(error current times the open loop inverting input resistance) that results (see Figure 29), a more exact low frequency closed loop transfer functions can be described as:
G G = G × RI RF R G 1+ 1+ + + F AO T O TO TO
for noninverting (G is positive) G 1 – G RF 1+ + AO TO
AC TRANSFER CHARACTERISTICS
The ac small signal transfer derivations below are based on a simplified single-pole model. Though inaccurate at frequencies approaching the closed-loop BW (CLBW) of the AD8011 at low noninverting external gains, they still provide a fair approximation and a intuitive understanding of its primary ac small signal characteristics.
for inverting (G is negative) +VS
For inverting operation and high noninverting gains these transfer equations provide a good approximation to the actual ac performance of the device.
To accurately quantify the VO vs. VP relationship, both AO(s) and TO(s) need to be derived. This can be seen by the following nonexpanded noninverting gain relationship:
VO (s) /VP (s) =
Z I = OPEN LOOP INPUT IMPEDANCE = CI || RL
G G AO [s]
Figure 29. ZI = Open-Loop Input Impedance
where G is the ideal gain as previously described. With R I = TO/AO (open-loop inverting input resistance), the second expression (positive G) clearly relates to the classical voltage feedback “op amp” equation with TO omitted do to its relatively much higher value and thus insignificant effect. AO and TO are the open-loop dc voltage and transresistance gains of the amplifier respectively. These key transfer variables can be described as:
RF TO [s]
with A (s) = O
R1 × gmf ×|A2| 1 – gmc × R1 Sτ1
1 – gmc × R1 80
(1 – gmc × R1)
and TO =
R1 × | A2| 2
- therefore RI =
Where gmc is the positive feedback transconductance (not shown) and 1/gmf is the thermal emitter resistance of devices D1/D2 and Q3/Q4. The gmc × R1 product has a design value that results in a negative dc open loop gain of typically –2500 V/V (see Figure 30). Though atypical of conventional CF or VF amps, this negative open-loop voltage gain results in an input referred error term (VP–VO/G = G/AO + RF/TO) that will typically be negative for G greater than +3/–4. As an example, for G = 10, AO = –2500 and TO = 1.2 MΩ, results in a error of –3 mV using the AV derivation above.
GAIN – dB Ohms
A = O
R1 × gmf × | A2|
PHASE – Degrees
FREQUENCY – Hz
Figure 30. Open-Loop Voltage Gain and Phase