# A noncommensurate line length modulator.

A Noncommensurate Line Length ModulatorIntroduction

There are many electronic applications that require amplitude modulation. Automatic leveling control loops and fast pulse modulation incorporate shunt PIN diodes to realize circuits that perform amplitude modulation. Typical circuits have PIN diodes spaced at equal intervals along a transmission line. These circuits have an ideal two-octave attenuation response centered about the frequency where the spacing betwen the diodes equals a quarter wavelength. Often this topology is used in applications requiring more than two octaves of bandwidth. In this case, the PIN diodes are spaced to achieve maximum attenuation at the high frequency end of the band. The diodes are biased with higher DC current to achieve the specified attenuation at the low frequency end of the required band.

This paper describes a modulator topology with a 2 to 26.5 GHz bandwidth and performance better than previous modulator designs. Improved performance is achieved by spacing the PIN diodes at unequal distances, thereby utilizing ripple cancellation to extend the bandwidth of the modulator, and embedding the diodes in a lowpass filter structure to minimize the insertion loss of the circuit. By using these techniques, the modulation performance of the microwave synthesized sweepers was optimized.

Theory of Operation

The modulator operates by placing a current-controlled impedance in shunt with a transmission line and switching this impedance from an open circuit to a short circuit. The modulator response can be analyzed by identifying two operating states. In the on-state, the PIN diodes are forward biased and appear as small shunt resistances across a transmission line. In this state, the RF power is attenuated. In the off-state, the PIN diodes are reversed biased and appear as small shunt capacitances across a transmission line. In this state, the RF power is transmitted.

Above a certain frequency related to the recombination rate and the physical properties of the PIN diode's I-layer, forward-bias current through the diode controls its RF resistance. In linear control systems, a constant current with respect to frequency should produce constant attenuation, that is, negative gain. In feedback systems, modulator gain influences the loop gain of the system. If the change in gain of the modulator in [delta]db/decade of control current does not change with frequency, then the loop gain of the system will not change with frequency and loop stability is maintained.

In pulsed RF systems, lower control current results in less stored charge in the I-layer reqion of the diode. The rise and fall times of the RF pulse envelope are dependent on the amount of charge stored in the I-layer region of the diode. A constant control current that achieves a constant attenuation across the entire frequency range will result in constant rise and fall times across the entire frequency range.

A Simplified Model of Modulator's On-State

This modulator design employs a ripple cancellation technique to achieve a bandwidth greater than that of a modulator using equally spaced diodes. The analysis of any modulator circuit requires a solution to a matrix equation. A five-diode modulator circuit requires the solution of a 5 X 5 matrix equation. Circuit simulator design tools can give the answer to this problem, but a more intuitive insight into the design problem can be gained by using the following first-order approximation.

One can consider any modulator as being a superposition of attenuation response created by any two diodes. A diode set is defined as any two adjacent diodes separated by a length of transmission line. The transfer function of a two-diode modulator can be solved using matrix techniques. For the maximum attenuation of two identical elements separated by a uniform transmission line with line, source and load impedances assumed to be equal, the attenuation across the circuit expressed in dB is, [Mathematical Expression Omitted] where x = the normalized shunt admittance [Mathematical Expression Omitted] [Theta] = the ratio of the test frequency to the frequency of

maximum attenuation [Theta] is normally expressed angularly as, [Mathematical Expression Omitted] Maximum attenuation occurs at, [Mathematical Expression Omitted] when the expression [V.sub.o]/[V.sub.a] is purely imaginary. Minimum attenuation occurs at, [Mathematical Expression Omitted] when the expression [V.sub.o]/[V.sub.a] is real.

Figure 1 shows the attenuation and frequency response of a two-diode modulator or a diode set. Designating the fundamental frequency of maximum attenuation as the center frequency [f.sub.c], maximum and minimum are reached in the attenuation response at odd and even multiples of the center frequency.

The new modulator topology separates the diodes at unequal intervals along a transmission line. The exact attenuation response of the modulator was analyzed using a microwave design system.

The matrix of the admittance transfer response of a five-diode modulator can be represented symbolically as, [Mathematical Expression Omitted] The diagonal coefficients are simply the normalized conductances of each diode at position n, n = 1, 2, 3, 4, 5. The terms adjacent to the diagonal define the transfer admittance response of the transmission line that connects the two adjacent diodes.

Figure 2 shows a simplified model of the five-diode modulator. The diodes are modeled as ideal conductances separated by ideal transmission lines. There are four primary diode sets contained within the modulator, including (1,2), (2,3), (3,4) and (4,5).

Figure 3 superimposes the attenuation responses of four primary diode sets. In this case, the length of the transmission line [T.sub.4] in diode set (4,5) is set to the quarter wavelength of the highest frequency in the band, [f.sub.c] = 26.5 GHz. Transmission line length [T.sub.1] in diode set (1,2) is set to an 18.5 GHz [f.sub.c]. [T.sub.2] in diode set (2,3) is set to two times the length of [T.sub.1] for an [f.sub.c] = 9 GHz. Diode set (1,2) will reach a maximum attenuation frequency when diode set (2,3) reaches a minimum attenuation frequency. [T.sub.3] in diode set (3,4) was set to three times the length of [T.sub.1] and has an [f.sub.c] = 4.5 GHz. In this case, diode set (3,4) is reaching a minimum attenuation frequency when diode set (1,2) is approaching a maximum attenuation frequency and diode set (2,3) is leaving a maximum attenuation frequency. Diode sets (2,3) and (4,5) are approaching a maximum attenuation frequency at 26.5 GHz while diode sets (1,2) and (3,4) are leaving a maximum attenuation frequency.

Figure 4 shows two predictions of the modulator's response. [I.sub.1] scales and adds the individual attenuation responses of the four primary diode sets previously described. [J.sub.1] is the exact solution of the five-diode modulator's response. The frequency points of minimum attenuation are set by the interaction of adjacent diodes and their quarter-wavelength spacing. The distance between these adjacent diodes will determine the resultant ripple characteristic.

The required frequency range of this design was 2 to 26.5 GHz. This design can be normalized to suit any required frequency range. The relative position of the diode sets to each other does not change the overall attenuation response of the modulator. The position of the diodes impacts the transmission response of the modulator.

A Simplified Model of the Modulator's Off-State

The off-state of the modulator is the second mode of operation that must be considered in the design of a broadband modulator. In this state, the diodes are reverse-biased and RF power is transmitted to the output of the circuit.

A shunt-diode modulator in the transmission mode of operation can be analyzed with classical filter theory. Figure 5 is a circuit diagram of the classical lowpass filter. The capacitance and inductance values are calculated from previously published works. The diodes are biased with a reverse voltage. In the reverse-bias state, the diodes are represented by shunt capacitances and the distances between the diodes are represented as series inductive elements. The insertion loss and cutoff frequency of the modulator's frequency response depend upon the diode-junction capacitance and the distances between the diodes. Without additional elements in the modulator circuit, a trade-off exists between the attenuation and transmission response of the modulator.

The new modulator topology minimizes the trade-off between the attenuation and transmission responses by embedding the diodes in a single high order lowpass filter. Figure 6 shows a model of the modulator showing additional elements in the circuit that realize a high order filter. Initial values of capacitance are based on values for a Chebyshev 0.5 dB ripple filter. The number of filter elements was determined by the maximum length that the transmission line segments could be while remaining below a quarter wavelength at 26.5 GHz and by a division of the spacing between the diodes. In this 35-element high order filter, a change in diode capacitance or bonding inductance only affects a small percentage of all the elements in the filter. In high order filter structures, the capacitor value of elements at the ends of the circuit converge to a single value and are small compared to the capacitance at the center of the filter. All the diodes have the same capacitance, so they are placed at the ends of the filter to realize these shunt capacitive elements.

In the five-diode modulator, four of the five diodes are placed at the end of the filter with the fifth diode placed off-center of the circuit. This diode does not fit into the filter as well as the other diodes since it should have a slightly higher capacitance. Radial stub lengths around this diode were optimized to give the smoothest filter response. Additional shunt capacitances and series inductances are realized by microstrip radial stubs and microstrip transmission lines. Transmission lines are 0.75 mm long, which places their quarter wavelength frequency well above the 26.5 GHz frequency band. Radial stubs are optimized to achieve the desired filter response with low insertion loss at 26.5 GHz. Again, a microwave design system linear circuit simulator and optimizer was used to find the optimum values of these elements.

This new modulator topology has distinct transmission advantages. The cut-off frequency of the transmission characteristic is determined primarily by the spacing between the radial stubs and not the diodes. The transmission response of the circuit is independent of the attenuation response of the modulator. The insertion loss is that of the ripple response of the filter, not of the diodes alone.

Circuit Realization

Figure 7 is a photograph of the complete modulator. The circuit is fabricated on 10 mil alumina microstrip. The five diodes are mounted in holes that are laser cut in the substrate for precise diode placement. The entire substrate is cemented to the grounded base plate by means of conductive epoxy cement. The diodes are chip mesa PIN diodes, which also are cemented with conductive epoxy to the base plate in the laser-cut holes. A bonded gold mesh is used to connect the diode anodes to the circuit pattern.

The DC bias is filtered with a lumped element five-pole Chebyshev lowpass filter with a cutoff frequency of 800 MHz. Series inductors are formed from 0.0015" diameter gold wire wound with five turns, each 0.012" in diameter. Shunt capacitors are 5.6 pF single-layer chip capacitors. The output filter is a seven-pole Chebyshev highpass filter with a cutoff frequency of 2 GHz. This circuit is fabricated on sapphire with planar process capacitors as the series elements and air wound coils as the shunt inductors.

The entire modulator assembly and biasing is built in a 3 X 4 mm housing to eliminate package modes in the operating frequency range. This improves the input-output isolation.

2 to 26.5 GHz Performance

The modulator circuit can be used in either linear or pulse modulation circuits. The choice of the proper diode with the necessary diode parameters will determine modulation rise and fall times, on-off ratio and gain. Figure 8 shows the maximum attenuation for the five-diode pulse modulator. The described five-diode pulse modulator had better than 95 dB on-off ratio from 2 to 20 GHz and better than 90 dB on-off ratio from 20 to 26.5 GHz. Figure 9 shows the rise and fall times of a pulsed waveform generated by the five-diode pulse modulator .2 ns rise and fall times are typical on a 25 ns wide pulse. Figure 10 shows the typical insertion loss of the linear modulator. Maximum loss at 26.5 GHz is 2.6 dB. Figure 11 shows a graph of the modulator attenuation at constant levels of bias current. The slope of these attenuation curves is related directly to change in loop gain with frequency when the modulator is used in ALC leveling loops.

Conclusion

Using ripple cancellation to extend bandwidth improves the frequency response of shunt diode modulators. The advantage of this device over previous AM modulator designs is that the current drive required to achieve a particular modulation is constant over a wider bandwidth. This constant gain makes the operation of control loops stable. In addition, the device requires a lower current to drive it to maximum attenuation and this device can change state more rapidly than previous designs. The rise and fall times of the pulsed RF envelope are improved since the diodes are not biased by high currents to obtain maximum attenuation. By embedding the modulator in a lowpass filter structure, the added length between the diodes is compensated for by additional filter elements. The insertion loss is dependent on the filter elements and not on the diode characteristics or the distance between diodes. This modulator topology effectively eliminates the trade-off between attenuation and insertion loss that constrained earlier designs. [Figures 1 to 11 Omitted]

References

[1] J.A. Hartman and T.L. Davis, "Design PIN Modulators with Wide Dynamic Range," Microwaves (USA), Vol. 15, No. 9, September 1976, pp. 42-46.

Mary K. Koenig received her BS degree in electrical engineering from the University of Washington in 1981. Currently, she is employed at Hewlett-Packard's Network Measurements Division, where she is involved in microwave circuit design and the research and development of precision synthesized microwave sources.

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Title Annotation: | microwave modulator |
---|---|

Author: | Koenig, Mary K. |

Publication: | Microwave Journal |

Date: | Mar 1, 1991 |

Words: | 2358 |

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