Amplifiers – With semiconductor amplifying device – Including plural stages cascaded
Reexamination Certificate
2002-02-27
2003-04-08
Choe, Henry (Department: 2817)
Amplifiers
With semiconductor amplifying device
Including plural stages cascaded
C330S110000, C330S308000
Reexamination Certificate
active
06545544
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of transimpedance amplifiers.
2. Prior Art
The Ideal Transimpedance Amplifier
A transimpedance amplifier converts an input current to an output voltage with a gain whose units are ohms.
FIG. 1
shows a circuit that uses an operational amplifier (opamp) and two resistors to make a negative feedback amplifier with an inverting voltage gain. For this circuit, the equation for v
o
and the amplifier voltage gain v
o
/v
i
is:
v
o
=−v
i
*RF/R
2
(Equation 1)
v
o
/v
i
=−RF/R
2
(Equation 2)
The circuit node at the noninverting input terminal of the amplifier in
FIG. 1
is a virtual ground. Because this node has zero impedance, the input network which consists of voltage source v
i
and resistor R
2
can be replaced with a current source that has a magnitude of i
in
=v
i
/R
2
. FIG.
2
. shows the modified amplifier circuit.
Equation 1 may be rewritten as:
v
o
=−RF
*(
v
i
/R
2
)=−
RF*i
in
(Equation 3)
The ideal transimpedance amplifier gain can be written as:
v
o
/i
in
=−RF
(Equation 4)
These equations have assumed that the amplifier has an infinite voltage gain. Since the ideal operational amplifier has no output voltage constraints, i
in
can be any magnitude (no overdrive condition). The magnitude of the gain of a real transimpedance amplifier is somewhat less than RF due to the finite gain of a real operational amplifier, and the input signal i
in
is limited in magnitude to the available output swing at v
o
divided by RF.
Feedback Theory and Stability
In classical feedback theory, the transfer function or closed-loop gain of a system with negative feedback is expressed as:
Transfer function=
G
/(1
+GH
) (Equation 5)
Where G is the gain in the forward path only and H is the gain in the feedback path only.
G and H are usually functions of frequency, that is, their magnitudes and their phase angles change with frequency. A common way of indicating this dependence is to write G and H as G(j&ohgr;) and H(j&ohgr;), where &ohgr; is radian frequency and j is {square root over (−1)}.
The most important quantity in determining the stability of a negative feedback amplifier is the GH term in the denominator of Equation 5. The system's loop gain (GH) is calculated with the feedback disconnected from the input summing node, but appropriately terminated. From Equation 5, if the loop gain GH equals −1 (magnitude of 1 and phase of −180°), the transfer function is undefined because of division by zero and the system is unstable. Actually, if the absolute value of the loop gain GH is equal to or greater than 1 at the frequency where the phase of GH=−180°, then the amplifier is unstable.
This concept is the key to analyzing the stability of transimpedance amplifiers, and particularly to understanding why transimpedance amplifiers can become unstable when diode clamps are used to provide input overdrive capability.
A Simple Transimpedance Amplifier
The simplest practical transimpedance amplifier is shown in FIG.
3
. Transistor Q
1
and resistor RL functionally replace the opamp in
FIG. 2
(the grounded emitter of the transistor may be considered the positive terminal of the opamp). The current in RF provides negative feedback from the amplifier's output to its input. The forward gain (G in Equation 5) of the amplifier is:
G=−&bgr;*RF||RL
(Equation 6)
Where &bgr; is the transistor current gain
The feedback gain (H in equation 5) is −1/RF, because the feedback is a current into the inverting amplifier input node. The loop gain is:
GH=&bgr;*RF||RL/RF=&bgr;*RL
/(
RL+RF
) (Equation 7)
Equation 7 expresses only the DC or low frequency loop gain. &bgr;, the transistor current gain, is really a function of frequency. Also there are capacitances in the circuit whose impedance is a function of frequency. The largest capacitance in this circuit that affects loop gain is C
cb
, the capacitance of the transistor base-collector junction. This capacitance is in parallel with RF and RL. A greatly simplified expression for the loop gain as a function of frequency is (neglecting any frequency dependence of H):
G
(
j
&ohgr;)
H
=&bgr;(
j
&ohgr;)*
RF||RL||(
1
/j&ohgr;C
cb
)/
RF
G
(
jω
)
H
=
β
(
jω
)
*
RF
&LeftDoubleBracketingBar;
RL
&RightDoubleBracketingBar;
(
1
/
jω
C
cb
)
/
RF
=
β
(
jω
)
*
RL
RL
+
RF
1
+
jω
C
cb
*
RL
*
RF
RL
+
RF
(
Equation
8
)
With respect to amplifier stability, one way to gain some insight is to set the feedback resistor RF to zero, that is, set the amplifier to have minimum gain, maximum feedback, and maximum bandwidth. If it's going to oscillate, it will oscillate under this condition. The result is:
G
(
j
&ohgr;)
H=P
(
j
&ohgr;) with
RF
=0 (Equation 9)
The capacitance C
cb
doesn't play a role, since it is shorted out. The only thing that matters is if &bgr;(j&ohgr;) is greater than one at a frequency where its phase is −180°. This is generally not the case, as otherwise, diode-connected transistors would oscillate.
Simple Transimpedance Amplifier with Overdrive Capability
The transimpedance amplifier in
FIG. 4
differs from that of
FIG. 3
in that Schottky diodes D
1
and D
2
have been added in parallel with feedback resistor RF. Without these clamping diodes, the magnitude of the input signal i
in
is limited to about (vcc−VCE
sat
)/RF. With the clamping diodes, when i
in
is in positive overdrive, transistor Q
1
turns on until the output voltage v
o
drops enough to forward bias Schottky diode D
2
, after which any additional input current i
in
passes through diode D
2
and transistor Q
1
to ground to maintain the output v
o
at one Schottky drop below the Vbe of transistor Q
1
. At the other extreme wherein i
in
is in negative overdrive, transistor Q
1
will turn off until the load resistor RL pulls the output voltage v
o
high enough to forward bias Schottky diode D
1
, after which any additional negative input current i
in
passes through Schottky diode D
1
to maintain the output v
o
at one Schottky diode drop above the Vbe of transistor Q
1
. Thus the diodes clamp the output voltage swing to 2*V
diode
peak to peak, even with large input signals or overdrive (note that the negative input current magnitude is ultimately limited by the resistor RL). When one of the diodes turns on, the effective feedback resistance drops from RF to R
diode
, which may be only a few ohms. Based on the analysis above (Equations 8 and 9), this reduction in gain and subsequent increase in bandwidth should not make the amplifier unstable.
A Buffered Transimpedance Amplifier with Overdrive Capability
FIG. 5
shows another common transimpedance amplifier topology that uses an emitter follower (transistor Q
2
) to buffer the load resistor RL from the feedback resistor RF. It has some advantages over the simple amplifier in FIG.
4
. First, the open loop gain is larger: instead of G=−&bgr;*RL||RF, it is:
G=−&bgr;*RL
(Equation 10)
The larger open loop gain increases the overall transimpedance gain. Second, when the output is taken at the emitter of Q
2
instead of at the collector of Q
1
, the amplifier has greater drive capability. The output voltages and output voltage swings are the same as for the transimpedance amplifier of FIG.
4
. The loop gain GH of this amplifier is (H is still −1/RF):
GH=&bgr;RL/RF
(Equation 11)
The loop gain of the amplifier without the emitter follower Q
2
was shown to be:
GH=&bgr;*RL
/(
RL+RF
) (Equation 7)
With RF>>RL, the difference in magnitude of the two equations is small. But when RF is very
Entrikin David W.
Link Garry Neal
Blakely , Sokoloff, Taylor & Zafman LLP
Choe Henry
Maxim Integrated Products Inc.
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