APPLICATION NOTE 3390

Abstract: In high-speed transmission-line applications, it is important to match the output impedance of a line driver to the line. While this is achieved usually with a resistor, an active impedance synthesis has advantages. Thisapplication note describes how to use positive feedback around an op amp to create the desired output impedance. Equations and circuit examples are given for low-noise audio, and video op amps driving 50Ω to 600Ω loads.

RF engineers require accurate 50Ω terminations for their coaxial cables, video transmission engineers require accurate 75Ω terminations for their cables, and broadcast engineers require accurate 600Ω terminations for their audio circuits. Other standard termination values are 110Ω, 120Ω and 500Ω. The termination requirements are not confined to analog signals. Digital signals depend on correct line termination for accurate, high-speed transmission throughout a system.

A serious disadvantage of the simple resistor approach is, however, the 6dB loss of signal between the buffer output and the terminated load. This results in a serious loss of signal headroom, particularly in single supply systems.

Note in Figure 1 that forward current into the load, I

Synthesised output impedance, R

The understanding here is that the closed-loop output impedance of the op amp is low enough over a wide enough bandwidth to be ignored. Thus the chosen resistances set the output impedance. In Figure 1, RΘ is the series resistor that sets the impedance looking back into the output of IC1. RΘ = R

Voltage Gain is given by:

Error term is given by:

Output Impedance is given by:

Error term is given by:

Errors due to finite open-loop gain (A

Assuming infinite open-loop gain from an ideal op amp.

Assuming infinite open-loop gain from an ideal op amp.

Figure 1 Advantage:

- Simplicity. Select RΘ to the required terminating value.
- Modest short-circuit protection.
- No interaction between R1-R2, and RΘ to a first order.
- Inverting and non-inverting gain operation allowed.

- 6dB minimum loss between the amplifier output pin (V'
_{O}) and the load driving point (V_{O}) when RΘ = R_{LOAD}(back terminated). Maximum output pk-pk voltage swing always less than half total power-supply voltage. - Doubled gain bandwidth required from the op amp.
- Open-loop output resistance of the op amp affects results at high frequencies.

Note in Figure 2 that forward current into the load, I

Synthesised output impedance R

The open-loop output resistance of the op amp is included to allow for the situation when R

Voltage Gain for Figure 2 is given by:

Error term is given by:

Output Impedance for Figure 2 is given by:

Errors due to finite open-loop gain of the op amp are shown.

Note that the overall input-to-output signal path in Figure 2 is inverting.

Assuming infinite open-loop gain from an ideal op amp, output impedance is:

Generally, the term [RΘ / [R3 + R4]] is << [1 + R2 / R1][1 + R4 / R3]

Assuming infinite open-loop gain from an ideal op amp, voltage gain is:

Rearranging the output impedance into the gain equation:

In general, R

Figure 2 Advantages:

- Significantly reduced loss between the amplifier output pin (V'
_{O}) and the load driving point (V_{O}). If RΘ = 0.1R_{LOAD}, loss is only 0.83dB. In other words, a significantly increased pk-pk output voltage swing for a given power supply, compared to the passive termination case. - Modest, short-circuit protection at main output.
- Easy to use.

- Positive and negative feedback coexist. Negative feedback must dominate at all times for stability.
- Interaction between R1-R4. Suitable for fixed-gain and termination conditions only.
- Inverting only practical operation.
- Positive feedback will tend to produce an increase in distortion performance over the purely negative feedback case.

Perhaps the obvious approach in Figure 3a is to set the value of R

A more accurate approach is to adjust R

|R

Practically, R

If the ratio is made 40dB:

|R

Care needs to be exercised when using the 40dB ratio, as the source voltage could be greater than the breakdown of the circuit under test. This is relevant when low-voltage op amps are under consideration.

A second method is to use a suitable network analyser.

A third method, specific to active impedance boosting techniques, is to measure the voltage and phase directly across the current-sense resistor RΘ. From the voltage difference, the synthesised output impedance is given by:

Referring to Figure 2.

Referring to Figure 2, and taking into account the effect of R3 and R4 in parallel with the output.

The incident or input drive voltage from the test source is V

By how much should RΘ be "boosted"? A practical upper limit is x10 (ie RΘ = 0.1 R

Ensure that the time constant of the negative feedback loop dominates the overall loop control. This means that the positive feedback loop ideally should roll off before the negative feedback loop. Referring to Figure 2, the first-order time constant (TC) of the negative feedback loop is:

The time constant of the positive feedback loop is:

C

This assumes that the capacitance at the op-amp inputs is greater than the parasitic capacitance of the feedback loop resistors. In wideband situations it is appropriate to split each of R1-R4 into two equal value resistors to effectively halve the parasitic capacitance.

If the circuit does not actually oscillate, there may be in-band response peaking. This can be checked by sweeping the circuit with a small signal (50mV to 100mV) sine wave to identify and plot the closed-loop frequency response (with load), and by correcting any in-band peaking by adjusting the feedback time constants.

Power supply = +5V

Gain = 1 (0dB)

R

Chose termination loss = 1dB.

The MAX4475 op-amp is chosen for its excellent distortion characteristics, bandwidth, and output drive capability. It is also unity-gain stable.

R

R

R2 = 0.25R1

Let R1 = 10k, then R2 = 2.5k. Use R2 = 2.4k + 100R. Then:

given that RΘ, and R

This ratio provides the boost to RΘ.

R4 = 0.428R3.

Let R3 = 10k. Then R4 = 4.28k. Use R4 = 4.3k.

Frequency (kHz) | Gain (dB) | Phase (Deg) |

100 | -0.3 | 5.6 |

220 | -0.5 | 14 |

430 | -1.0 | 23 |

580 | -1.5 | 29 |

710 | -2.0 | 33 |

830 | -2.5 | 37 |

940 | -3.0 | 39 |

1050 | -3.5 | 47 |

1170 | -4.0 | 52 |

1370 | -5.0 | 62 |

Frequency (kHz) | dB (across 6.2kΩ) | R_{OUT} (Ω) |

100 | -21.5 | 517 |

220 | -21.8 | 502 |

430 | -22.4 | 468 |

580 | -23.2 | 429 |

710 | -24 | 392 |

830 | -24.6 | 364 |

940 | -25.2 | 340 |

1050 | -26 | 313 |

1170 | -26.6 | 287 |

1370 | -28 | 249 |

Calculated gain = -0.18dB with values shown above.

Calculated output impedance = 572Ω. This value is determined by R3+R4 || R

Power supply = +5V.

Gain = 1 (0dB).

R

Chose termination loss = 1dB.

The MAX4265 op amp is chosen for its excellent distortion characteristics, bandwidth, and output drive capability. It is also unity-gain stable.

For 1dB termination loss.

R

R2 = 0.272R1.

Let R1=1k. Then R2=272R. Use R2=270R as nearest preferred value. Then:

when RΘ and R

This ratio provides the boost to RΘ.

R4=0.472R3.

Let R3=1k. Then R3 = 472R. Use R3=470R as nearest preferred.

Frequency (MHz) | Gain (dB) | Phase (Deg) |

1.0 | -0.3 | 0 |

2.0 | -0.3 | -3.5 |

4.0 | -0.4 | -10.25 |

6.0 | -0.7 | -16.5 |

8.0 | -1.0 | -23.5 |

10.0 | -1.3 | -30 |

15.0 | -2.3 | -44 |

20.0 | -3.5 | -58 |

30.0 | -7.0 | 87 |

Frequency (MHz) | dB Across 510Ω | Phase (Deg) | R_{OUT} (Ω) |

1.0 | -21 | -3.2 | 45.4 |

2.0 | -21 | -4.4 | 45.4 |

4.0 | -21 | -7.25 | 45.4 |

8.0 | -21.8 | -14.5 | 41.45 |

10 | -22.1 | -15.5 | 40 |

20 | -23.7 | -21 | 33.3 |

Calculated Gain = -0.63dB with values shown above, and taking into account additional 50Ω source resistance not included in R1.

Calculated Output Impedance = 45.5Ω. This value is determined by R3 + R4 || R

Expressions have been developed to help gain an insight into the effects of open-loop gain and output impedance on the final closed-loop performance. Examples of the circuits have been built and demonstrate the ease of use of the circuits given.