Bandwidth limiting for amplifiers

An apparatus for limiting the bandwidth of an amplifier provides for the design of an input impedance, a feedback impedance, and a load impedance such that the load impedance is proportional to the sum of the input impedance and feedback impedance. A sampling circuit has a load impedance including a resistor and capacitor in series to reduce the effective amplifier transconductance, which decreases bandwidth without increasing noise density or making this circuit more difficult to drive than a conventional circuit.

FIELD OF THE INVENTION

The present invention relates to amplifiers, more specifically to limiting the bandwidth of amplifiers.

BACKGROUND INFORMATION

Amplifiers are widely used in analog circuits, particularly for analog-to-digital converters (“ADCs”). ADCs convert an analog signal to a digital signal by sampling the analog signal, processing it, and converting it to a digital signal. One important property of sampling circuits is bandwidth. Because an analog signal is one comprised of many frequencies, the larger the bandwidth of the sampling circuit, the greater the range of frequencies that may be captured by the sampling circuit. The analog signal is then passed to a signal processor that ultimately outputs a digital signal. In analog circuit design, there is a trade-off between bandwidth and noise. As bandwidth increases, more signal information can be processed. However, a larger bandwidth also permits more noise to pass through the filter, and more noise power must then be tolerated by the signal processor. Therefore, as a general design principle, an analog circuit should be of the minimum bandwidth necessary to process the required signal with specified accuracy.

Limiting the bandwidth of circuits to the minimum required for processing the input reduces the noise sampled, which is beneficial for signal processing. This is illustrated with two examples. First, the sampling bandwidth of a switched-capacitor sampling circuit, as inFIG. 1A, is typically designed to be three to four times the maximum required input frequency to obtain good gain and phase flatness over the input range. However, if the maximum required input frequency is reduced by a factor of four, then ideally the sampling bandwidth should also be reduced by a factor of four. The reduced bandwidth would minimize the total noise power sampled from any circuitry driving the sampling circuit. Second, when an amplifier in feedback is used as an active sampling circuit, as inFIG. 1B, the bandwidth is typically designed to be ten times the maximum required input frequency to maintain good AC linearity (i.e., a spurious-free output) for all required input frequencies. Although the required bandwidth is wider relative to the signal frequency of the switched-capacitor sampling circuit, the amplifier should still be designed with the minimum bandwidth necessary, also for noise considerations. Both examples illustrate that regardless of the application, bandwidth should be limited for noise considerations.

Information relevant to attempts to address these problems can be found in U.S. Pat. No. 7,298,151. However, in the circuit of U.S. Pat. No. 7,298,151 (shown asFIG. 2), the DC gain is limited by how large the load resistive element (RL)208can be made. This is because the DC gain from the input204of the transconductor to the output205is set by gmRL, where gmis the transconductance of the amplifier212. Although there are many applications in which high DC gain is desirable, high DC gain is difficult to achieve, because DC gain is limited by how large RLcan be made. If RLis too large, the circuit has issues related to parasitic capacitances including feedback loop instability.

In conventional circuit design, there are several ways to limit bandwidth. Two of the most common are described. In the first method, capacitance is increased to shunt some resistance in the signal path. In the example described above of the sampling circuit, as inFIG. 1A, this is accomplished by increasing the capacitance of sampling capacitor114. In the example of the active sampling circuit, as inFIG. 1B, this is also accomplished by increasing the capacitance of sampling capacitor106. However, one disadvantage of increasing capacitance, particularly at the input to the circuit, is the increased difficulty for the preceding circuit to drive the larger capacitive load, which may in turn increase the amount of overshoot and ringing at the output, and cause the driving circuit to be unstable.

Another way of limiting bandwidth in conventional circuit design is increasing resistance in series with the signal. In the circuit shown inFIG. 2, this is accomplished by increasing resistance in sampling switch211. In an active sampling circuit, this is typically accomplished by decreasing the transconductance of the main amplifier input device. However, one disadvantage of increasing resistance is that it is accompanied by an increase in noise density. The noise of the sampling circuits in the presence of increased resistance is typically unchanged. Therefore, as the resistance increases, the bandwidth decreases, causing the noise density to increase. These effects offset each other. Furthermore, if some subsequent circuit has a fixed bandwidth, higher noise density results in increased overall noise.

Thus, there remains a need in the art for a way to limit the bandwidth of an amplifier that does not require either increasing the capacitance or increasing the resistance, which both negatively impact the performance of the circuit.

SUMMARY

An apparatus is described herein that provides for a circuit limiting the bandwidth of an amplifier. The circuit includes an amplifier, an input impedance, a feedback impedance, and a load impedance. The load impedance includes resistive and capacitive elements. In the exemplary embodiments according to the present invention, by fixing substantially constant the ratio of the load impedance to the sum of the feedback impedance and input impedance, the closed-loop bandwidth of the system is reduced due to the reduction of the effective amplifier transconductance. However, because the actual transconductance has not been reduced, the noise density of the amplifier is not increased. The input impedance also remains unchanged, which makes this circuit no more difficult to drive than a conventional circuit.

Advantages of the present invention include: neither increasing capacitance at the input to the amplifier (which would make the circuit difficult to drive) nor increasing resistance (which would increase the noise density of the circuit), and eliminating the penalties associated with lower transconductance amplifiers or increased switch resistance.

DETAILED DESCRIPTION

The subject invention will now be described in detail for specific preferred embodiments of the invention, it being understood that these embodiments are intended only as illustrative examples and the invention is not to be limited thereto.

FIG. 3shows an exemplary circuit according to the present invention. The circuit includes an amplifier312with its non-inverting input303tied to a reference potential309, which may be ground (typically for a single-ended implementation) or a non-zero potential (typically for a differential implementation). An input impedance (ZIN)306is coupled to the inverting input302of amplifier312. A feedback impedance (ZF)307is coupled to the output305of amplifier312and the inverting input302. A load impedance (ZL)308is coupled to the output305of amplifier312and reference potential309. Input impedance306, feedback impedance307, and load impedance308are abstractions of any combination of resistances and capacitances.

FIG. 4shows an exemplary circuit having a load impedance414comprising a resistor411and a capacitor413connected in series, according to an embodiment of the present invention. InFIG. 4, exemplary circuit elements have been provided for impedance blocks306,307, and308ofFIG. 3. Resistors and/or capacitors406produce input impedance408, a resistor407produces feedback impedance410, and a resistor411and capacitor413connected in series produces load impedance414. M represents any value selected in the design of the circuit to scale load resistor411and load capacitor413. This circuit decreases bandwidth without decreasing the input impedance, decreasing the amplifier transconductance, or increasing the output noise density. This is accomplished by reducing the effective amplifier transconductance.

Because an ideal transconductance amplifier has infinite input and output impedances, current flowing out of the amplifier must either flow through feedback resistor407or load resistor411. At high frequencies, capacitors act as short circuits (capacitor impedance approaches zero as frequency approaches infinity). Thus, load capacitor413will act as a short circuit to ground (or a reference potential)409, and input resistors and/or capacitors406acts as a short circuit to the input potential, which is ideally a zero impedance source. The circuit ofFIG. 4will then become a current divider formed by feedback resistor407and load resistor411. The total amplifier current is represented by (iT)420. A portion of the amplifier current will flow through load resistor411to ground409, which is represented by load current (iL)417. The remaining portion of the amplifier current will flow back to the input source404through feedback resistor407, which is represented by feedback current (iF)416. The formula for a current divider provides that iL, the portion of the current flowing through load resistor411is

MM+1×iT.
The portion of the current flowing through feedback resistor407, iF, is

1M+1×iT
(in other words, iF+iL equals the total amplifier output current). Even if the input voltage source were not an ideal voltage source, the current split ratio is adjusted somewhat, but the overall function remains the same. Furthermore, load resistor411may be adjusted to account for a non-zero source resistance such that the current split ratio is maintained exactly as desired.

At low frequencies, capacitors have very large impedances that dominate over resistance. However, the feedback current (iF)416flowing through feedback resistor407remains

1M+1×iT,
and the portion of the current flowing through load resistor411remains

MM+1×iT.
The current-splitting ratio remains substantially constant for all frequencies, because the load impedance414is M times smaller than the impedance410in the feedback path.

Given that only a portion of the amplifier output current is flowing through the feedback path as represented by iF416, the effective amplifier transconductance is reduced by a factor of

1M+1.
For an amplifier connected in a negative feedback loop, the closed loop bandwidth is proportional to the transconductance of the loop, where the loop transconductance is defined as the ratio of the change in current that flows through the feedback loop in response to a change in voltage at the amplifier input. Because the current splitting ratio causes only a small portion of the amplifier output current to be directed back through the feedback path, the bandwidth of the system is reduced by the same factor,

1M+1.
However, because the actual amplifier transconductance has not been altered, the noise density of the amplifier is not increased (voltage thermal noise density is proportional to transconductance), and there is no penalty in terms of noise density. Moreover, the input impedance is unchanged, which makes this circuit no more difficult to drive than a conventional circuit.

So long as ZLis designed to have a comparable or lower impedance than the total impedance of the feedback path (ZF+ZIN) for all frequencies of interest (in other words, the ratio of ZLto (ZF+ZIN) is less than or equal to 1), bandwidth will be limited. When ZL<(ZF+ZIN), substantially more amplifier output current flows to the load impedance and not to the feedback path, reducing the effective amplifier transconductance, which in turn reduces the loop bandwidth.

FIG. 5shows an exemplary sampling circuit according to an embodiment of the present invention. It is the circuit ofFIG. 4with an added switch510. Switch510is connected in series with feedback resistor507. When switch510is opened, the charge on sampling capacitor506is frozen and a sample is taken. The load resistor508and load capacitor513solves the issue of noise at output node505and on sampling capacitor506being dominated by switch resistance as described above.

FIG. 6shows an exemplary switched-capacitor discrete time integrator according to an embodiment of the present invention. The operation of the switches samples charge on capacitor606, then transfers it to feedback capacitor607, where the charge is integrated. During the sampling phase, switches617and621are on, sampling the input voltage on input capacitor606. During the transfer phase, switches617and621are off, and switch620is on, transferring the sampled charge on capacitor606to feedback capacitor607. The integrator may be periodically reset with the feedback switch608and switch618. Feedback resistor (RF)610may be used to control the dynamics of the reset period. In this embodiment of the invention, the shunt load path616is a scaled version of the feedback path611. The input impedance615and feedback impedance611are determined by the desired transfer function of the circuit. This embodiment of the invention (as well asFIG. 5above) illustrate that various forms of impedances and switches may be used. Switches may be replicated (and scaled) on load path616and controlled in the same manner. For example, when feedback switch608is on, an added load switch618is also on, and vice versa. An additional load switch may be coupled to the load capacitor614and reference potential609if switch resistance is large relative to resistors610and613. Switch619may be placed in series with load capacitor614to match the switching characteristic of input impedance615. For a further example, a continuous time integrator could be designed to have a resistive input impedance306and a capacitive feedback impedance307.

The exemplary embodiments above show circuits with a ratio fixed for all frequencies. However, the ratio need not be constant for all frequencies. For example, the relation could be:
ZL=f(x)(ZF+ZIN)
where f(x) is a function of the input frequency. There remains a fixed relationship between ZLand (ZF+ZIN), but the ratio varies with input frequency. For example, inFIG. 4, if load capacitor413has a value of MC, but load resistor411had a smaller value of

RF2⁢M,
at very low frequencies, the feedback current (iF)416would be

1M+1.
At very high frequencies, the feedback current would be even lower as

12⁢M+1.
This would provide optimized noise or loop performance. The exemplary embodiments above show single-ended circuits, but it will be appreciated that the same principles hold for differential circuits as well. For example,FIG. 6includes an amplifier612with its non-inverting input609tied to a reference potential, which may be ground for a single-ended implementation or a non-zero potential for a differential implementation. Alternative embodiments with an inverting input of the amplifier tied to reference potential and a non-inverting input of the amplifier tied to the input or load impedance are possible as well. Alternative embodiments having an amplifier with a single input are possible as well.

The descriptions and illustrations of the embodiments above should be read as exemplary and not limiting. Modifications, variations, and improvements are possible in light of the teachings above and the claims below, and are intended to be within the spirit and scope of the invention.